------
## 最终结论
```python
def min_product_tuple(tuples_list):
    products = [a * b for a, b in tuples_list]
    return min(products)

# Test cases
assert min_product_tuple([(2, 7), (2, 6), (1, 8), (4, 9)]) == 8
assert min_product_tuple([(10, 20), (15, 2), (5, 10)]) == 30
assert min_product_tuple([(11, 44), (10, 15), (20, 5), (12, 9)]) == 100
```