Answer
${x^{-2}y^{2}}$ = $\frac{y^{2}}{x^{2}}$
Work Step by Step
$(\frac{x^{\frac{1}{2}}y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}})^{-4}$
= $({x^{\frac{1}{2}}y^{-\frac{7}{4} +\frac{5}{4}}})^{-4}$
= $({x^{\frac{1}{2}}y^{-\frac{2}{4}}})^{-4}$
= $({x^{\frac{1}{2}\times-4}y^{-\frac{2}{4}\times-4}})$
= $({x^{-2}y^{2}})$
= $\frac{y^{2}}{x^{2}}$
