Answer
$\displaystyle \frac{y^2}{x^4}$
Work Step by Step
We simplify:
$\displaystyle \frac{(x^{-2}y^{3})^{4}}{(x^{2}y^{-5})^{-2}}$
First we distribute the exponents:
$\displaystyle \frac{(x^{-8}y^{12})}{(x^{-4}y^{10})}$
Now we combine like exponents:
$x^{-8--4}y^{12-10}$
$x^{-8+4}y^{12-10}$
$x^{-4}y^{2}$
$\displaystyle \frac{y^2}{x^4}$