🔗 Problem

Problem: What is the value of 5^4?

Gemma 2B:

    5^4 means 5 multiplied by itself four times: 5 * 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125
    125 * 5 = 625

    ### Answer: 625

Expected answer: 625

Correct? Yes

🔗 Follow-up

Problem: What would the result be if instead of raising 5 to the 4th power, you raised the number 4 to the 4th power?

Gemma 2B:

    Raising 4 to the 4th power means multiplying 4 by itself four times: 4 * 4 * 4 * 4.

    4 * 4 = 16
    16 * 4 = 64
    64 * 4 = 256

    ### Answer: 256

Expected answer: 256

Correct? Yes

🔗 Problem

Problem: What is 9 raised to the power of 3?

Gemma 2B:

    9 raised to the power of 3 means 9 multiplied by itself three times: 9 * 9 * 9.

    9 * 9 = 81
    81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: What would the outcome be if we raise 6 to the power of 3, instead of 9?

Gemma 2B:

    6 raised to the power of 3 means 6 multiplied by itself three times: 6 * 6 * 6.

    6 * 6 = 36
    36 * 6 = 216

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Problem

Problem: What is the cube of 5?

Gemma 2B:

    The cube of a number is that number multiplied by itself three times. So, the cube of 5 is:

    5 x 5 x 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: What is the value if we are cubing 7 instead of 5?

Gemma 2B:

    The cube of 7 is 7 multiplied by itself three times:

    7 x 7 x 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the result of raising 9 to the power of 2?

Gemma 2B:

    Raising a number to the power of 2 means multiplying the number by itself. So, 9 to the power of 2 is 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we raise 8 to the power of 2 instead of 9?

Gemma 2B:

    8 to the power of 2 means multiplying 8 by itself: 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: Determine the value of 3 to the power of 3.

Gemma 2B:

    3 to the power of 3 means 3 multiplied by itself three times: 3 * 3 * 3.

    3 * 3 = 9
    9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the value of 3 to the power of 3. Now, consider what would happen if the base was 5 instead of 3. What is the value of 5 to the power of 3?

Gemma 2B:

    5 to the power of 3 means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the value when 9 is raised to the power of 2?

Gemma 2B:

    9 raised to the power of 2 means 9 multiplied by itself 2 times.  This is written as 9² and calculated as 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: Considering our previous problem, if instead of 9 we raise 4 to the power of 2, what would be the value?

Gemma 2B:

    Raising 4 to the power of 2 means multiplying 4 by itself 2 times. This is written as 4² and calculated as 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: Calculate the result of 9^2.

Gemma 2B:

    9² means 9 multiplied by itself: 9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: After learning about the calculation of 9^2, can you now tell me what is the result of 7^2?

Gemma 2B:

    7² means 7 multiplied by itself: 7 * 7 = 49

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: Determine the value of 10^3.

Gemma 2B:

    10^3 means 10 multiplied by itself three times: 10 * 10 * 10.

    10 * 10 = 100
    100 * 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Follow-up

Problem: If we changed the base in the previous question to 4 while keeping the exponent as 3, what value would we get for 4^3?

Gemma 2B:

    4^3 means 4 multiplied by itself three times: 4 * 4 * 4.

    4 * 4 = 16
    16 * 4 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: What is the value of 6 squared, or 6^2?

Gemma 2B:

    6 squared, or 6^2, means 6 multiplied by itself: 6 * 6.

    6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: What would the value be if instead of 6, we have 4 squared or 4^2?

Gemma 2B:

    4 squared, or 4^2, means 4 multiplied by itself: 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the result of 3 raised to the power of 3?

Gemma 2B:

    3 raised to the power of 3 means 3 multiplied by itself three times: 3 * 3 * 3.

    3 * 3 = 9
    9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we found the cube of 3. Now, what would be the value if we raise 6 to the power of 3 instead?

Gemma 2B:

    6 raised to the power of 3 means 6 multiplied by itself three times: 6 * 6 * 6.

    6 * 6 = 36
    36 * 6 = 216

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Problem

Problem: What is 10 raised to the power of 2?

Gemma 2B:

    10 raised to the power of 2 means 10 multiplied by itself twice: 10 * 10.

    10 * 10 = 100

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: What happens if we instead consider 4 raised to the power of 2?

Gemma 2B:

    4 raised to the power of 2 means 4 multiplied by itself twice: 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the value of 9 raised to the power of 3?

Gemma 2B:

    9 raised to the power of 3 means 9 multiplied by itself three times: 9 x 9 x 9.

    9 x 9 = 81
    81 x 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: Earlier, we found out the value for 9 raised to the third power, right? Now, considering the same scenario, what would be the value if you raise 5 instead of 9 to the power of 3?

Gemma 2B:

    You are correct! We found that 9 raised to the third power is 729.

    Now, we want to find the value of 5 raised to the third power, which means 5 multiplied by itself three times: 5 x 5 x 5.

    5 x 5 = 25
    25 x 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the value of 2^2?

Gemma 2B:

    2^2 means 2 multiplied by itself, or 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: In the previous situation we evaluated the square of 2. Now, consider what would the value be if instead of 2, we needed to evaluate the square of 5?

Gemma 2B:

    The square of 5, denoted as 5², means 5 multiplied by itself, or 5 * 5.

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Problem

Problem: What is the value when the number 7 is raised to the power of 2?

Gemma 2B:

    Raising a number to the power of 2 means multiplying the number by itself. So, 7 raised to the power of 2 is 7 * 7.

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, what would be the value if we raised the number 2 to the power of 2 instead of 7?

Gemma 2B:

    Following the same logic, raising 2 to the power of 2 means multiplying 2 by itself. So, 2 to the power of 2 is 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: What is the value of 8 raised to the power of 3?

Gemma 2B:

    8 raised to the power of 3 means 8 multiplied by itself three times: 8 * 8 * 8.

    8 * 8 = 64
    64 * 8 = 512

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we evaluated 8 raised to the power of 3. What if we changed the base and considered 7 instead of 8? What is the value of 7 raised to the power of 3?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the value of 3^2?

Gemma 2B:

    3^2 means 3 multiplied by itself: 3 * 3.

    3 * 3 = 9

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: Now, what if instead you were to calculate the square of 8? What would be the value of 8^2?

Gemma 2B:

    8^2 means 8 multiplied by itself: 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: What is the value when 9 is raised to the power of 2?

Gemma 2B:

    9 raised to the power of 2 means 9 multiplied by itself, or 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: What would be the result if instead of raising 9 to the power of 2, we raised 6 to the power of 2?

Gemma 2B:

    6 raised to the power of 2 means 6 multiplied by itself, or 6 * 6.

    6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: What is the value of 5 cubed?

Gemma 2B:

    5 cubed means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: What is the value if we consider a cube with a side length of 8 units instead of 5 units?

Gemma 2B:

    The volume of a cube is calculated by cubing the side length. So, for a cube with a side length of 8 units, the volume would be:

    8 * 8 * 8 = 512 cubic units.

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Problem

Problem: What is the outcome when 5 is raised to the power of 2?

Gemma 2B:

    5 raised to the power of 2 means 5 multiplied by itself two times: 5 * 5.

    5 * 5 = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: What is the outcome when 4 is raised to the power of 2, instead of 5?

Gemma 2B:

    4 raised to the power of 2 means 4 multiplied by itself two times: 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the value when you raise 5 to the power of 2?

Gemma 2B:

    Raising a number to the power of 2 means multiplying the number by itself. So, 5 to the power of 2 is 5 * 5.

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: Following from the previous problem, what would be the value if we raised 8 to the power of 2 instead of 5?

Gemma 2B:

    Raising 8 to the power of 2 means multiplying 8 by itself: 8 * 8.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power of 3?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself three times: 2 x 2 x 2.

    2 x 2 = 4
    4 x 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: You previously calculated 2 raised to the power of 3. Now, what would be the result if we raise 10 to the power of 3 instead?

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 x 10 x 10.

    10 x 10 = 100
    100 x 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Problem

Problem: What is the result of 1^3?

Gemma 2B:

    1 raised to the power of 3 means multiplying 1 by itself three times: 1 * 1 * 1 = 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Given what you have learned, what happens if you take the new number 3 and raise it to the power of 3 instead?

Gemma 2B:

    3 raised to the power of 3 means multiplying 3 by itself three times: 3 * 3 * 3 = 27.

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: What is the value of 1 raised to the power of 9?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself. Therefore, 1 raised to the power of 9 is still 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What would the result be if we change the exponent from 9 to 6 and compute the value of 1 raised to the power of 6 instead?

Gemma 2B:

    Regardless of the exponent, any number raised to the power of 1 will always equal 1. So, 1 raised to the power of 6 is still 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the result of 8^3?

Gemma 2B:

    8^3 means 8 multiplied by itself three times: 8 * 8 * 8.

    8 * 8 = 64
    64 * 8 = 512

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Follow-up

Problem: Previously, we raised 8 to the power of 3. Now, what if we raise 5 to the power of 3, what would be the result?

Gemma 2B:

    5 to the power of 3 means 5 multiplied by itself three times: 5 * 5 * 5

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the result when 1 is raised to the power of 2?

Gemma 2B:

    1 raised to the power of 2 means 1 multiplied by itself, or 1 * 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Given the understanding that 1 raised to the power of 2 gives us 1, what would be the result if we raised 4 to the power of 2 instead?

Gemma 2B:

    4 raised to the power of 2 means 4 multiplied by itself, or 4 * 4.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the result of 2^2?

Gemma 2B:

    2^2 means 2 multiplied by itself: 2 * 2 = 4

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Previously, you evaluated 2^2. Now, what's the result of performing an identical operation, but instead of squared (2^2), it is raised to the 7th power (2^7)?

Gemma 2B:

    2^7 means 2 multiplied by itself seven times: 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128

    ### Answer: 128

Expected answer: 128

Correct? Yes

🔗 Problem

Problem: What is 8 raised to the power of 2?

Gemma 2B:

    8 raised to the power of 2 means 8 multiplied by itself 2 times:

    8² = 8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we took one instead of eight and raised it to the power of 2?

Gemma 2B:

    1 raised to the power of 2 means 1 multiplied by itself 2 times:

    1² = 1 * 1 = 1

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power of 3?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself 3 times: 2 * 2 * 2.

    2 * 2 = 4
    4 * 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: What would the result be if you raised 7 to the power of 3 instead of 2 in the previous problem?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself 3 times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the value of 8^2?

Gemma 2B:

    8² means 8 multiplied by itself, or 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: What would be the value if you squared 1 instead of 8?

Gemma 2B:

    1 squared, or 1², means 1 multiplied by itself: 1 * 1.

    1 * 1 = 1

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the result of 6 to the power of 3?

Gemma 2B:

    6 to the power of 3 means 6 multiplied by itself three times: 6 x 6 x 6.

    6 x 6 = 36
    36 x 6 = 216

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what would be the result if we evaluate 6 to the power of 1 instead of 3?

Gemma 2B:

    Any number raised to the power of 1 is simply itself.

    Therefore, 6 to the power of 1 is 6.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: What is the value when 7 is raised to the power of 1?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself.

    Therefore, 7 raised to the power of 1 is equal to 7.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Follow-up

Problem: Now, consider what will be the value when 7 is not just raised to the power of 1, but to the power of 3 instead?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself three times: 7 * 7 * 7.

    Let's calculate:

    * 7 * 7 = 49
    * 49 * 7 = 343

    Therefore, 7 raised to the power of 3 is equal to 343.

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power of 2?

Gemma 2B:

    2 raised to the power of 2 means 2 multiplied by itself: 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the result of 2 raised to the power of 2. Now, what is the result of 4 raised to the power of 2?

Gemma 2B:

    4 raised to the power of 2 means 4 multiplied by itself: 4 * 4.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the value of 4^2?

Gemma 2B:

    4^2 means 4 multiplied by itself, or 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: Following up on our previous question, what would be the result if we raised 10, instead of 4, to the power of 2?

Gemma 2B:

    Raising 10 to the power of 2 means multiplying 10 by itself:

    10^2 = 10 * 10 = 100

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: What is the value of 9^2?

Gemma 2B:

    9² means 9 multiplied by itself: 9 * 9.

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: What would be the value if instead of 9^2, we calculated 4^2?

Gemma 2B:

    4² means 4 multiplied by itself: 4 * 4.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the value of 5^3?

Gemma 2B:

    5^3 means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: What is the value if we consider raising 7 to the power of 3 instead of 5^3?

Gemma 2B:

    7 to the power of 3, written as 7³, means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the result when 7 is raised to the power of 3?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself 3 times.

    7 to the power of 3 = 7 x 7 x 7 = 49 x 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What would be the result if instead of raising 7 to the power of 3, you raised 9 to the power of 3?

Gemma 2B:

    9 raised to the power of 3 means 9 multiplied by itself 3 times.

    9 to the power of 3 = 9 x 9 x 9 = 81 x 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Problem

Problem: What is the calculation result of 2^2?

Gemma 2B:

    2^2 means 2 multiplied by itself, or 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of 2 units, you only had a single unit. What would be the result if you squared that single unit (1^2)?

Gemma 2B:

    1 squared, or 1^2, means 1 multiplied by itself: 1 * 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the value when 4 is raised to the power of 3?

Gemma 2B:

    Raising a number to the power of 3 means multiplying that number by itself three times.

    So, 4 raised to the power of 3 is: 4 x 4 x 4 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Now imagine if we raised 3 to the power of 3 instead, what would be the result?

Gemma 2B:

    Raising 3 to the power of 3 means multiplying 3 by itself three times: 3 x 3 x 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: Calculate the value of 2^3.

Gemma 2B:

    2^3 means 2 multiplied by itself three times: 2 * 2 * 2.

    2 * 2 = 4
    4 * 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we evaluated 2^3. Now consider if it were 3^3 instead. What value would that give?

Gemma 2B:

    3^3 means 3 multiplied by itself three times: 3 * 3 * 3.

    3 * 3 = 9
    9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: What is the value of 5^4?

Gemma 2B:

    5^4 means 5 multiplied by itself 4 times.

    So, 5^4 = 5 * 5 * 5 * 5 = 25 * 5 * 5 = 125 * 5 = 625

    ### Answer: 625

Expected answer: 625

Correct? Yes

🔗 Problem

Problem: What is the value of 7^3?

Gemma 2B:

    7^3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What would the value be if we have 6^3 instead of 7^3?

Gemma 2B:

    6^3 means 6 multiplied by itself three times: 6 * 6 * 6

    6 * 6 = 36
    36 * 6 = 216

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Problem

Problem: What is the value of 10^2?

Gemma 2B:

    10^2 means 10 multiplied by itself 2 times: 10 * 10.

    10 * 10 = 100

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: What is the result if we have 8 groups, not 10, of spiders, each group having a power of 2?

Gemma 2B:

    Here's how to solve this:

    * **Power of 2:** Each group of spiders has a power of 2.  This means each group has 2 spiders.
    * **Total spiders:** We have 8 groups, and each group has 2 spiders, so there are 8 * 2 = 16 spiders in total.

    ### Answer: 16

Expected answer: 64

Correct? No

🔗 Problem

Problem: What is the value of 1 raised to the power of 2?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself.  Similarly, any number raised to the power of 0 is equal to 1.

    Therefore, 1 raised to the power of 2 is equal to 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What if, instead of 1, the base was changed to 6? What would be the result of 6 raised to the power of 2?

Gemma 2B:

    6 raised to the power of 2 means 6 multiplied by itself twice: 6 * 6.

    6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: Find the value of 9^3.

Gemma 2B:

    9^3 means 9 multiplied by itself three times: 9 * 9 * 9.

    9 * 9 = 81
    81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: Now consider this: What would be the result if we were to raise 7 to the power of 3 instead of 9? Calculate 7^3.

Gemma 2B:

    7^3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is 1^2 equal to?

Gemma 2B:

    1 squared (1²) means 1 multiplied by itself: 1 * 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What is 3^2? In other words, if now you're considering 3 instances of a number being multiplied by itself instead of the single instance we previously evaluated, what would the new result be?

Gemma 2B:

    3 squared (3²) means 3 multiplied by itself: 3 * 3.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: What is the result when you evaluate 2 raised to the power 2?

Gemma 2B:

    2 raised to the power of 2 means 2 multiplied by itself: 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: What would the result be if we now consider 1 raised to the power 2 instead of 2 raised to the power 2?

Gemma 2B:

    1 raised to the power of 2 means 1 multiplied by itself: 1 * 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the result when 4 is squared?

Gemma 2B:

    Squaring a number means multiplying it by itself. So, 4 squared is 4 * 4.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: What happens to the result when instead of squaring 4, you square 7?

Gemma 2B:

    When you square 7, you multiply 7 by itself, resulting in 7 * 7 = 49.

    So, when you square 7 instead of 4, the result increases from 16 to 49.

    ### Answer: The result increases.

Expected answer: 49

Correct? No

🔗 Problem

Problem: What is the value of 7 raised to the power of 3?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we raise 8 instead of 7 to the power of 3?

Gemma 2B:

    8 raised to the power of 3 means 8 multiplied by itself three times: 8 * 8 * 8.

    8 * 8 = 64
    64 * 8 = 512

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Problem

Problem: What is the value of 4^3?

Gemma 2B:

    4^3 means 4 multiplied by itself three times: 4 * 4 * 4.

    4 * 4 = 16
    16 * 4 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, consider that instead of taking 4^3, we take 5^3. What is now the value?

Gemma 2B:

    5^3 means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the value of 1^2?

Gemma 2B:

    1 squared (1²) is equal to 1 multiplied by itself: 1 * 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What would be the value if you raised 7 to the power of 2 instead of 1?

Gemma 2B:

    7 to the power of 2 (7²) means 7 multiplied by itself: 7 * 7.

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: What is the result of computing 6^2?

Gemma 2B:

    6^2 means 6 multiplied by itself, or 6 * 6.

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: Suppose you originally had 3 square blocks instead of 6. What is the result of squaring the number of these blocks now, i.e., what is 3^2?

Gemma 2B:

    3^2 means 3 multiplied by itself, or 3 * 3.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power of 2?

Gemma 2B:

    2 raised to the power of 2 means 2 multiplied by itself: 2 * 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we calculated the square of 2. But what if we had 3 instead of 2 to begin with? What would be the result of 3 raised to the power of 2?

Gemma 2B:

    3 raised to the power of 2 means 3 multiplied by itself: 3 * 3.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: What is the value of 4^2?

Gemma 2B:

    4^2 means 4 multiplied by itself, or 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: Now, consider what will be the value if instead of 4, we square 9? What will 9^2 be?

Gemma 2B:

    9^2 means 9 multiplied by itself, or 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Problem

Problem: What is the value of 3^2?

Gemma 2B:

    3^2 means 3 multiplied by itself, or 3 * 3.

    3 * 3 = 9

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what if, instead of 3, we raised 8 to the power of 2? What would be the value?

Gemma 2B:

    8 to the power of 2 means 8 multiplied by itself, or 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: What is the value of 10 raised to the power of 3?

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 * 10 * 10.

    10 * 10 = 100
    100 * 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Problem

Problem: What is the result of 10 raised to the power of 3?

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 * 10 * 10.

    10 * 10 = 100
    100 * 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we change the base number from 10 to 9, and compute 9 raised to the power of 3?

Gemma 2B:

    9 raised to the power of 3 means 9 multiplied by itself three times: 9 * 9 * 9.

    9 * 9 = 81
    81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Problem

Problem: What's the value of 8^1?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself.

    Therefore, 8^1 = 8.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: Following our previous calculation, let's change the numbers a bit. What's the value now if we evaluate 10^1?

Gemma 2B:

    As with any number raised to the power of 1, the result is simply the number itself.

    Therefore, 10^1 = 10.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: What is the result of 7 to the power of 3?

Gemma 2B:

    7 to the power of 3 means 7 multiplied by itself three times: 7 * 7 * 7.

    * 7 * 7 = 49
    * 49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What if instead of elevating 7 to the power of 3, we changed the base and elevated 2 to the power of 3? What would be the result then?

Gemma 2B:

    2 to the power of 3 means 2 multiplied by itself three times: 2 * 2 * 2.

    * 2 * 2 = 4
    * 4 * 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power of 2?

Gemma 2B:

    2 raised to the power of 2 (written as 2²) means multiplying 2 by itself: 2 x 2.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: What happens if we consider 6 instead of 2 and raise it to the power of 2?

Gemma 2B:

    6 raised to the power of 2 (written as 6²) means multiplying 6 by itself: 6 x 6.

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: What is the value of 5 raised to the power of 3?

Gemma 2B:

    5 raised to the power of 3 means 5 multiplied by itself three times.

    This can be written as 5 x 5 x 5.

    5 x 5 = 25
    25 x 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: Next, consider what happens if instead of 5, we have 4 in the base. What would be the new value if 4 is raised to the power of 3?

Gemma 2B:

    Similar to the previous calculation, 4 raised to the power of 3 means 4 multiplied by itself three times.

    This can be written as 4 x 4 x 4.

    4 x 4 = 16
    16 x 4 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: What is the value of raising 5 to the power of 4?

Gemma 2B:

    Raising 5 to the power of 4 means multiplying 5 by itself four times: 5 * 5 * 5 * 5.

    * 5 * 5 = 25
    * 25 * 5 = 125
    * 125 * 5 = 625

    ### Answer: 625

Expected answer: 625

Correct? Yes

🔗 Follow-up

Problem: Consider the original finding where we raised 5 to the power of 4. Now, what would be the result if we raised 1 to the power of 4 instead?

Gemma 2B:

    Raising 1 to any power always results in 1.  This is because multiplying 1 by itself any number of times will always give you 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the result of 3 raised to the power of 5?

Gemma 2B:

    3 raised to the power of 5 means multiplying 3 by itself 5 times:

    3 x 3 x 3 x 3 x 3 = 243

    ### Answer: 243

Expected answer: 243

Correct? Yes

🔗 Follow-up

Problem: Considering the previous problem where we calculated 3^5, what would be the result if we instead calculated 2^5?

Gemma 2B:

    2 raised to the power of 5 means multiplying 2 by itself 5 times:

    2 x 2 x 2 x 2 x 2 = 32

    ### Answer: 32

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: What would be the output of 2^2?

Gemma 2B:

    2^2 means 2 multiplied by itself: 2 * 2 = 4

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we raised 5 to the power of 2 instead of 2?

Gemma 2B:

    5 to the power of 2 means 5 multiplied by itself: 5 * 5 = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Problem

Problem: What is the value of 4^2?

Gemma 2B:

    4^2 means 4 multiplied by itself, or 4 * 4.

    4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: What would be the value if originally, instead of 4^2, it was calculated as 9^2?

Gemma 2B:

    9^2 means 9 multiplied by itself, or 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Problem

Problem: What is the value of 6^2?

Gemma 2B:

    6^2 means 6 multiplied by itself, or 6 * 6.

    6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: What would be the value if we considered 7^2 instead of 6^2?

Gemma 2B:

    7^2 means 7 multiplied by itself, or 7 * 7.

    7 * 7 = 49

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: What is the result of 10^3?

Gemma 2B:

    10^3 means 10 multiplied by itself three times: 10 * 10 * 10.

    This equals 100 * 10 = 1000.

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Follow-up

Problem: What is the result if we replace the base number from the previous problem (which was 10), with 7? In other words, what is the value of 7^3?

Gemma 2B:

    7^3 means 7 multiplied by itself three times: 7 * 7 * 7.

    This equals 49 * 7 = 343.

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the value of 4 ^ 2 in mathematics?

Gemma 2B:

    In mathematics, the expression  4 ^ 2 means 4 raised to the power of 2, which is the same as 4 multiplied by itself:

    4 ^ 2 = 4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: Following up from your last computation, how would the outcome change if you raised 6 to the power of 2 instead of 4?

Gemma 2B:

    Raising 6 to the power of 2 means multiplying 6 by itself:

    6 ^ 2 = 6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: What is the outcome when 10 is raised to the power of 3?

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 * 10 * 10.

    This equals 100 * 10 = 1000.

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Follow-up

Problem: What would be the outcome if instead of 10, we raised 1 to the power of 3?

Gemma 2B:

    1 raised to the power of 3 means 1 multiplied by itself three times: 1 * 1 * 1.

    This equals 1 * 1 = 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: What is the value of 7 raised to the power of 3?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself 3 times: 7 * 7 * 7

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: Following up from the previous question, what would the result be if we raised 3 to the power of 3 instead of 7?

Gemma 2B:

    3 raised to the power of 3 means 3 multiplied by itself 3 times: 3 * 3 * 3

    3 * 3 = 9
    9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: What is the result of 8 raised to the power of 2?

Gemma 2B:

    8 raised to the power of 2 means 8 multiplied by itself: 8 * 8 = 64.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: What would the result be if instead of raising 8 to the power of 2, we raised 7 to the power of 2?

Gemma 2B:

    7 raised to the power of 2 means 7 multiplied by itself: 7 * 7 = 49

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: What is the cubed value of 7?

Gemma 2B:

    The cubed value of a number is found by multiplying the number by itself three times.

    So, the cubed value of 7 is 7 * 7 * 7 = 343.

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What would be the result if instead of cubing 7, you cubed 6?

Gemma 2B:

    To cube 6, we multiply it by itself three times: 6 * 6 * 6.

    This gives us 36 * 6 = 216.

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Problem

Problem: What is the result of 8 raised to the power of 2?

Gemma 2B:

    8 raised to the power of 2 means 8 multiplied by itself twice: 8 * 8 = 64.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Considering the same calculation, what is the result if we raise 6 to the power of 2 instead of 8?

Gemma 2B:

    6 raised to the power of 2 means 6 multiplied by itself twice: 6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: What is the result of 2 raised to the power 3?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself 3 times: 2 * 2 * 2.

    This equals 8.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: Previously, you computed the value of 2 raised to the power 3. Now, calculate what happens if you raise 5 to the power 3 instead.

Gemma 2B:

    5 raised to the power of 3 means 5 multiplied by itself 3 times: 5 * 5 * 5.

    This equals 125.

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: Calculate the value of 5 raised to the power of 2.

Gemma 2B:

    5 raised to the power of 2 means 5 multiplied by itself 2 times.  This is written as 5² and calculated as:

    5² = 5 * 5 = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: In continuation of the previous problem, now calculate the value of 4 raised to the power of 2.

Gemma 2B:

    4 raised to the power of 2 means 4 multiplied by itself 2 times. This is written as 4² and calculated as:

    4² = 4 * 4 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: What is the result when 7 is raised to the power of 2?

Gemma 2B:

    Raising a number to the power of 2 means multiplying the number by itself.  So, 7 raised to the power of 2 is:

    7 * 7 = 49

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Follow-up

Problem: What would happen if instead of 7, we raised 10 to the power of 2?

Gemma 2B:

    If we raised 10 to the power of 2, we would be multiplying 10 by itself:

    10 * 10 = 100

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: What is the value of 10 raised to the power of 2?

Gemma 2B:

    10 raised to the power of 2 means 10 multiplied by itself 2 times: 10 * 10 = 100.

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: Now consider what happens if instead of raising 10 to the power of 2, we instead raise 2 to the power of 2. What would be the value?

Gemma 2B:

    2 raised to the power of 2 means 2 multiplied by itself 2 times: 2 * 2 = 4

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: What is the value of 6^2?

Gemma 2B:

    6^2 means 6 multiplied by itself, or 6 * 6.

    6 * 6 = 36

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: What would be the value if you raise 9 to the power of 2 instead of 6?

Gemma 2B:

    9 to the power of 2 means 9 multiplied by itself, or 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Problem

Problem: What is the value of the expression 3^3?

Gemma 2B:

    The expression 3^3 means 3 multiplied by itself three times: 3 * 3 * 3.

    3 * 3 = 9
    9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: What would be the result if, instead of 3, we raised 5 to the power of 3?

Gemma 2B:

    5 to the power of 3 means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the result when you calculate 1^3?

Gemma 2B:

    1 raised to the power of 3 (1³) means multiplying 1 by itself three times: 1 * 1 * 1.

    Any number multiplied by 1 remains the same. So, 1 * 1 * 1 = 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What would be the result if we raised 9 to the power of 3 instead of 1?

Gemma 2B:

    9 raised to the power of 3 (9³) means multiplying 9 by itself three times: 9 * 9 * 9.

    9 * 9 = 81
    81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Problem

Problem: What is the result of 3 raised to the power of 6?

Gemma 2B:

    3 raised to the power of 6 means multiplying 3 by itself six times:

    3 x 3 x 3 x 3 x 3 x 3 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: What would be the value if we instead raised 3 to the power of 1?

Gemma 2B:

    Any number raised to the power of 1 is simply itself.

    So, 3 raised to the power of 1 is just 3.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: What is the value of 3^5?

Gemma 2B:

    3^5 means 3 multiplied by itself five times: 3 * 3 * 3 * 3 * 3.

    Let's calculate:

    * 3 * 3 = 9
    * 9 * 3 = 27
    * 27 * 3 = 81
    * 81 * 3 = 243

    ### Answer: 243

Expected answer: 243

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what would be the result if we consider 3 raised to the power of 1?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself. This is because raising a number to the power of 1 simply means multiplying the number by itself once.

    Therefore, 3 raised to the power of 1 (3^1) is equal to 3.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: What is the cubic value of 8, expressed as 8^3?

Gemma 2B:

    The cubic value of 8, expressed as 8^3, means 8 multiplied by itself three times:

    8^3 = 8 * 8 * 8 = 64 * 8 = 512

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Follow-up

Problem: What is the result if instead of cubic value of 8, we calculate the cubic value of 1, expressed as 1^3?

Gemma 2B:

    The cubic value of 1, expressed as 1^3, means 1 multiplied by itself three times:

    1^3 = 1 * 1 * 1 = 1

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Calculate the value of 9^2.

Gemma 2B:

    9^2 means 9 multiplied by itself: 9 * 9.

    9 * 9 = 81

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: Following our previous calculation of 9^2, let's change the number. What is the value of 5^2?

Gemma 2B:

    5^2 means 5 multiplied by itself: 5 * 5.

    5 * 5 = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Problem

Problem: What is the exponential value of 2 to the power of 2?

Gemma 2B:

    2 to the power of 2 means 2 multiplied by itself: 2 * 2.

    2 * 2 = 4

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: What is the result if the base 2 is raised to the power of 1 instead of 2?

Gemma 2B:

    Any number raised to the power of 1 equals itself.  So, 2 to the power of 1 is simply 2.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Calculate the value of 5 squared.

Gemma 2B:

    5 squared means 5 multiplied by itself: 5 * 5 = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: If we reconsider the previous concept but instead use 3 as the base, what would be the value of 3 squared?

Gemma 2B:

    3 squared means 3 multiplied by itself: 3 * 3 = 9

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: What is the value of 8 raised to the power 2?

Gemma 2B:

    8 raised to the power of 2 means 8 multiplied by itself twice: 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: What is the square of 7?

Gemma 2B:

    The square of a number means multiplying the number by itself.

    Therefore, the square of 7 is 7 * 7.

    7 * 7 = 49

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: What is the value when 8 is raised to the power of 3?

Gemma 2B:

    8 raised to the power of 3 means 8 multiplied by itself three times: 8 x 8 x 8.

    8 x 8 = 64
    64 x 8 = 512

    ### Answer: 512

Expected answer: 512

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the value when 8 was raised to the power of 3. What would the value be if instead we raise 7 to the power of 3?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself three times: 7 x 7 x 7.

    7 x 7 = 49
    49 x 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the value of 3 raised to the power of 3?

Gemma 2B:

    3 raised to the power of 3 means 3 multiplied by itself three times: 3 x 3 x 3.

    3 x 3 = 9
    9 x 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: What happens if we change the situation a bit and instead of 3, we use 2 and raise it to the power of 3? What would be the result?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself three times: 2 x 2 x 2.

    2 x 2 = 4
    4 x 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: What is the cube of 9?

Gemma 2B:

    The cube of a number is that number multiplied by itself three times.

    So, the cube of 9 is 9 * 9 * 9 = 81 * 9 = 729.

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: What would the cube be if we considered 3 instead of 9?

Gemma 2B:

    The cube of 3 is 3 * 3 * 3 = 9 * 3 = 27

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: What is the result of raising 9 to the third power?

Gemma 2B:

    Raising a number to the third power means multiplying the number by itself three times.

    So, 9 to the third power is 9 * 9 * 9 = 81 * 9 = 729.

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the result of raising 9 to the third power. Now, what if instead of raising 9, you raise 3 to the third power? What would be the result then?

Gemma 2B:

    Raising 3 to the third power means multiplying 3 by itself three times: 3 * 3 * 3.

    This simplifies to 9 * 3, which equals 27.

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

Problem: What is the result of 6 raised to the power of 3?

Gemma 2B:

    6 raised to the power of 3 means 6 multiplied by itself three times: 6 * 6 * 6.

    * 6 * 6 = 36
    * 36 * 6 = 216

    ### Answer: 216

Expected answer: 216

Correct? Yes

🔗 Follow-up

Problem: "What would be the result if instead of raising 6 to the power of 3, we raised 10 to the power of 3?"

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 * 10 * 10.

    * 10 * 10 = 100
    * 100 * 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Problem

Problem: What is 9 squared, or 9^2?

Gemma 2B:

    9 squared, or 9^2, means 9 multiplied by itself: 9 * 9.

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: What would the result be if we squared a smaller number, like 4^2?

Gemma 2B:

    4 squared, or 4^2, means 4 multiplied by itself: 4 * 4.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: Evaluate the expression 5^3.

Gemma 2B:

    The expression 5^3 means 5 multiplied by itself three times: 5 * 5 * 5.

    5 * 5 = 25
    25 * 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Problem

Problem: What is the value of 8 raised to the power of 2?

Gemma 2B:

    8 raised to the power of 2 means 8 multiplied by itself 2 times: 8 * 8.

    8 * 8 = 64

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous question, what would be the value if instead of 8 raised to the power of 2, we now have 10 raised to the power of 2?

Gemma 2B:

    10 raised to the power of 2 means 10 multiplied by itself 2 times: 10 * 10.

    10 * 10 = 100

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: What is the value when 10 is raised to the power of 3?

Gemma 2B:

    10 raised to the power of 3 means 10 multiplied by itself three times: 10 * 10 * 10.

    10 * 10 = 100
    100 * 10 = 1000

    ### Answer: 1000

Expected answer: 1000

Correct? Yes

🔗 Follow-up

Problem: Based on the previous problem, let's consider a different scenario. What will be the value when 2 raised to the power of 3 instead of 10?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself three times: 2 * 2 * 2.

    2 * 2 = 4
    4 * 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: What is the value of 9 raised to the power of 3?

Gemma 2B:

    9 raised to the power of 3 means 9 multiplied by itself three times: 9 * 9 * 9.

    9 * 9 = 81
    81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Follow-up

Problem: Now reflect on the previous problem but this time think about what would happen if it was 7 that was raised to the power of 3. What would be the value then?

Gemma 2B:

    7 raised to the power of 3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Problem

Problem: What is the value of 7^3?

Gemma 2B:

    7^3 means 7 multiplied by itself three times: 7 * 7 * 7.

    7 * 7 = 49
    49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: What would be the result if there was only 1 number instead of 7, and it was raised to the power of 3?

Gemma 2B:

    If there was only one number, say "x", and it was raised to the power of 3, it would be represented as x³.

    The result would be x multiplied by itself three times: x * x * x.

    It's important to remember that any number raised to the power of 3 is simply that number multiplied by itself three times.

    ### Answer: x³ = x * x * x

Expected answer: 1

Correct? No

🔗 Problem

Problem: What is the value of 5 raised to the power of 3?

Gemma 2B:

    5 raised to the power of 3 means 5 multiplied by itself three times: 5 x 5 x 5.

    5 x 5 = 25
    25 x 5 = 125

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we evaluated what happens when 5 is raised to the power of 3. Now, suppose we had started with 2 instead of 5. What would be the result if 2 were raised to the power of 3?

Gemma 2B:

    2 raised to the power of 3 means 2 multiplied by itself three times: 2 x 2 x 2.

    2 x 2 = 4
    4 x 2 = 8

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: What is the value of 7^3?

Gemma 2B:

    7^3 means 7 multiplied by itself three times: 7 * 7 * 7.

    * 7 * 7 = 49
    * 49 * 7 = 343

    ### Answer: 343

Expected answer: 343

Correct? Yes

🔗 Follow-up

Problem: Following on from the previous question, what would the outcome be if we replaced 7 with 9 in our exponent calculation? In other words, what is the value of 9^3?

Gemma 2B:

    9^3 means 9 multiplied by itself three times: 9 * 9 * 9

    * 9 * 9 = 81
    * 81 * 9 = 729

    ### Answer: 729

Expected answer: 729

Correct? Yes

🔗 Problem

Problem: What is the result when 1 is raised to the 5th power?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself.

    Therefore, 1 raised to the 5th power is still 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: What would be the result if 1 is raised to the 9th power instead of the 5th power?

Gemma 2B:

    Any number raised to the power of 1 is equal to itself. This rule applies regardless of the exponent.

    Therefore, 1 raised to the 9th power is still 1.

    ### Answer: 1

Expected answer: 1

Correct? Yes