Answer
$\dfrac{n^{10}}{25m^{18}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{5m^4n^{-3}}{m^{-5}n^2} \right)^{-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5^{-2}m^{4(-2)}n^{-3(-2)}}{m^{-5(-2)}n^{2(-2)}}
\\\\=
\dfrac{5^{-2}m^{-8}n^{6}}{m^{10}n^{-4}}
\\\\=
5^{-2}m^{-8-10}n^{6-(-4)}
\\\\=
5^{-2}m^{-8-10}n^{6+4}
\\\\=
5^{-2}m^{-18}n^{10}
\\\\=
\dfrac{n^{10}}{5^{2}m^{18}}
\\\\=
\dfrac{n^{10}}{25m^{18}}
.\end{array}
