Answer
$\dfrac{m^{4}}{27}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{3^{-1}m^4(m^2)^{-1}}{3^2m^{-2}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3^{-1}m^4m^{2(-1)}}{3^2m^{-2}}
\\\\=
\dfrac{3^{-1}m^4m^{-2}}{3^2m^{-2}}
\\\\=
3^{-1-2}m^{4+(-2)-(-2)}
\\\\=
3^{-3}m^{4-2+2}
\\\\=
\dfrac{m^{4}}{3^{3}}
\\\\=
\dfrac{m^{4}}{27}
.\end{array}