Answer
$\dfrac{s^{2}}{81r^{4}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(3rs)^{-2}}{3^2r^2s^{-4}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3^{-2}r^{-2}s^{-2}}{3^2r^2s^{-4}}
\\\\=
3^{-2-2}r^{-2-2}s^{-2-(-4)}
\\\\=
3^{-2-2}r^{-2-2}s^{-2+4}
\\\\=
3^{-4}r^{-4}s^{2}
\\\\=
\dfrac{s^{2}}{3^{4}r^{4}}
\\\\=
\dfrac{s^{2}}{81r^{4}}
.\end{array}