Answer
$\displaystyle \frac{x^{3}}{y^{2}}$
Work Step by Step
$(\displaystyle \frac{x^{-5/4}y^{1/3}}{x^{-3/4}})^{-6}=(\frac{x^{-5/4}}{x^{-3/4}}\cdot y^{1/3})^{-6}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=(x^{-5/4-(-3/4)}\cdot y^{1/3})^{-6}$
...$-\displaystyle \frac{5}{4}+\frac{3}{4}=\frac{-2}{4}=-\frac{1}{2}$
$=(x^{-1/2}y^{1/3})^{-6}\qquad$... apply $(ab)^{n}=a^{n}b^{n}$
$=x^{(-1/2)(-6)}y^{(1/3)(-6)}$
$=x^{3}y^{-2}\qquad$... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$
$=\displaystyle \frac{x^{3}}{y^{2}}$
