1. \( \frac{\sqrt[4]{\left(a^{2} b^{2}\right)^{6}}}{a^{5} b^{7} \times a^{-2} b^{-4}} \)

To simplify the expression \( \frac{\sqrt[4]{\left(a^{2} b^{2}\right)^{6}}}{a^{5} b^{7} \times a^{-2} b^{-4}} \), start with simplifying the numerator. The term \( \left(a^{2} b^{2}\right)^{6} = a^{12} b^{12} \), so taking the fourth root gives us \( \sqrt[4]{a^{12} b^{12}} = a^{3} b^{3} \). Now, simplify the denominator: \[ a^{5} b^{7} \times a^{-2} b^{-4} = a^{5 - 2} b^{7 - 4} = a^{3} b^{3}. \] Thus, the overall expression becomes: \[ \frac{a^{3} b^{3}}{a^{3} b^{3}} = 1. \] The simplified expression is \( 1 \).