Answer
$\displaystyle \frac{y^{2}}{x^{2}}$
Work Step by Step
$(\displaystyle \frac{x^{1/2}y^{-7/4}}{y^{-5/4}})^{-4}=(x^{1/2}\cdot\frac{y^{-7/4}}{y^{-5/4}})^{-4}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=(x^{1/2}\cdot y^{-7/4-(-5/4)})^{-4}$
$=(x^{1/2}\cdot y^{-2/4})^{-4}$
$=(x^{1/2}\cdot y^{-1/2})^{-4} \qquad$... apply $(ab)^{n}=a^{n}b^{n}$
$=x^{(1/2)(-4)}\cdot y^{(-1/2)(-4)}$
$=x^{-2}y^{2}\qquad$... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$
$=\displaystyle \frac{y^{2}}{x^{2}}$
