Answer
$ \frac{x^{3}}{y^{2}} $.
Work Step by Step
The given expression is
$\left ( \frac{x^{-\frac{5}{4}}y^{\frac{1}{3}}}{x^{-\frac{3}{4}}} \right )^{-6}$
Use $\frac{1}{a^n}=a^{-n}$
$=\left ( x^{-\frac{5}{4}}y^{\frac{1}{3}}\cdot x^{\frac{3}{4}} \right )^{-6}$
Use $a^m\cdot a^n= a^{m+n}$.
$=\left ( x^{-\frac{5}{4}+\frac{3}{4}}y^{\frac{1}{3}} \right )^{-6}$
$=\left ( x^{\frac{-5+3}{4}}y^{\frac{1}{3}} \right )^{-6}$
$=\left ( x^{\frac{-2}{4}}y^{\frac{1}{3}} \right )^{-6}$
$=\left ( x^{\frac{-1}{2}}y^{\frac{1}{3}} \right )^{-6}$
Use $(ab)^m=a^mb^m$.
$ =x^{\frac{6}{2}}y^{\frac{-6}{3}} $
$ =x^{3}y^{-2} $
Use $a^{-n}=\frac{1}{a^n}$
$ =\frac{x^{3}}{y^{2}} $.
