Answer
$\dfrac{x^{8}}{y^4}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left(\dfrac{x^{-3}y^2}{x^5y^{-2}}\right)^{-1}
$, is equivalent to
\begin{align*}\require{cancel}
&
\left(x^{-3-5}y^{2-(-2)}\right)^{-1}
&(\text{use }\dfrac{x^m}{x^n}=x^{m-n})
\\\\&=
\left(x^{-8}y^{2+2}\right)^{-1}
\\\\&=
\left(x^{-8}y^{4}\right)^{-1}
\\\\&=
x^{-8(-1)}y^{4(-1)}
&(\text{use }\left(x^m\right)^n=x^{mn})
\\\\&=
x^{8}y^{-4}
\\\\&=
x^{8}\cdot\dfrac{1}{y^4}
&(\text{use }a^{-m}=\dfrac{1}{a^m})
\\\\&=
\dfrac{x^{8}}{y^4}
.\end{align*}
Hence, the expression $\left(\dfrac{x^{-3}y^2}{x^5y^{-2}}\right)^{-1}
$ simplifies to $
\dfrac{x^{8}}{y^4}
$.
