Answer
$\dfrac{4k^{5}}{m^2}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(2k)^2m^{-5}}{(km)^{-3}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2^2k^2m^{-5}}{k^{-3}m^{-3}}
\\\\=
4k^{2-(-3)}m^{-5-(-3)}
\\\\=
4k^{2+3}m^{-5+3}
\\\\=
4k^{5}m^{-2}
\\\\=
\dfrac{4k^{5}}{m^2}
.\end{array}