------
## 最终结论
```python
def max_product_tuple(tuples_list):
    max_product = 0
    for a, b in tuples_list:
        product = a * b
        if product > max_product:
            max_product = product
    return max_product

# Test cases
assert max_product_tuple([(2, 7), (2, 6), (1, 8), (4, 9)]) == 36
assert max_product_tuple([(10,20), (15,2), (5,10)]) == 200
assert max_product_tuple([(11,44), (10,15), (20,5), (12, 9)]) == 484
```