Here I go one more that I'm really not sure of, what I really hate is that we have all that practice homework but none of the exercise where as complexe as those in the actual homework, so I basically have no reference...

$\displaystyle

\left( \frac {x^{-1}(x-y)^3 \sqrt[4]{y^3}}{x^{-4}y \sqrt {(x-y)}} \right)^{-2}

$

$\displaystyle \left( x^{-1-(-4)}(x-y)^{\frac {3}{1}-\frac {1}{2}}{\color{red}(y^{\frac{3}{4}-1})} \right)^{-2}

$

$\displaystyle \left( x^3(x-y)^{\frac {6}{2}-\frac {1}{2}}{\color{red}(y^{-\frac{1}{4}})} \right)^{-2}

$

$\displaystyle \left( x^3(x-y)^{\frac {5}{2}} {\color{red}(y^{-\frac{1}{4}})} \right)^{-2}

$

$\displaystyle \left( x^3(x-y)^{\frac {5}{2}}{\color{red}y^{-\frac {1}{4}} }\right)^{-2}

$

$\displaystyle x^{-6}(x-y)^{-5}{\color{red}y^{\frac{1}{2}}}$

Can I simplify this even further? The answer cannot contain fractions or radicals.

Thank you so much, for all the help, I'm eternaly greatful!