Q: What is the value of $2^{0^{1^9}} + (2^0)^{1^9}$?
A:
Step 1: Evaluate the first term $2^{\left(0^{\left(1^9\right)}\right)}$
- First, simplify the exponent's base: $1^9 = 1$.
- Then, calculate $0^1 = 0$.
- Finally, compute $2^0 = 1$.

Step 2: Evaluate the second term $\left(\left(2^0\right)^1\right)^9$
- Simplify inside the parentheses: $2^0 = 1$.
- Then, $(1)^1 = 1$.
- Raise $1$ to the power of $9$: $1^9 = 1$.

Step 3: Add the results of the two terms
- $1 + 1 = 2$.
Thus, the value of the expression is $\boxed{2}$.


Q: Chandler wants to buy a $500$ dollar mountain bike. For his birthday, his grandparents send him $50$ dollars, his aunt sends him $35$ dollars and his cousin gives him $15$ dollars. He earns $16$ dollars per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike?
A:
Step 1. **Identify the total amount of money Chandler needs:** Chandler wants to buy a mountain bike that costs $500.

Step 2. **Calculate the total amount of birthday money Chandler received:**
- From his grandparents: $50$
- From his aunt: $35$
- From his cousin: $15$
- Total birthday money: $50 + 35 + 15 = 100$

Step 3. **Set up an equation for the total money Chandler will have after $x$ weeks of saving his earnings from the paper route:**
- He earns $16$ per week from his paper route.
- Total money after $x$ weeks: Birthday money + Earnings from paper route = $100 + 16x$

Step 4. **Formulate the equation based on the cost of the mountain bike:**
- The total money should equal the cost of the bike: $100 + 16x = 500$

Step 5. **Solve the equation for $x$:**
- Subtract $100$ from both sides of the equation: $16x = 500 - 100$
- Simplify the right side: $16x = 400$
- Divide both sides by $16$: $x = \frac{400}{16}$
- Simplify the division: $x = 25$

Step 6. **Conclusion:** Chandler will be able to buy the mountain bike after saving for $25$ weeks.
The answer is $\boxed{25}$.


Q: Six rectangles each with a common base width of $2$ have lengths of $1, 4, 9, 16, 25$, and $36$. What is the sum of the areas of the six rectangles?
A:
Step 1. **Identify the dimensions of each rectangle**: Each rectangle has a common base width of $2$. The lengths of the rectangles are given as $1, 4, 9, 16, 25$, and $36$.

Step 2. **Calculate the area of each rectangle**: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of each rectangle can be calculated as follows:
- For the rectangle with length $1$: Area = $2 \times 1 = 2$
- For the rectangle with length $4$: Area = $2 \times 4 = 8$
- For the rectangle with length $9$: Area = $2 \times 9 = 18$
- For the rectangle with length $16$: Area = $2 \times 16 = 32$
- For the rectangle with length $25$: Area = $2 \times 25 = 50$
- For the rectangle with length $36$: Area = $2 \times 36 = 72$

Step 3. **Sum the areas of all rectangles**: Add the areas calculated in the previous step:
\[
\text{Total Area} = 2 + 8 + 18 + 32 + 50 + 72
\]

Step 4. **Simplify the sum**: Add the numbers to find the total area:
\[
\text{Total Area} = 2 + 8 + 18 + 32 + 50 + 72 = 182
\]
Therefore, the sum of the areas of the six rectangles is $\boxed{182}$.

=== End of Example ===

Instruction for the next problem:
When solving the next question, please explicitly follow the same format as the above example:
- MUST Use Step 1:, Step 2:, Step 3:, etc.
- MUST NOT generate new questions, examples, verification code, or explanations beyond this problem.
- MUST end your answer with the final value inside \boxed{}.

Q: