Answer
$\dfrac{2m^{10}}{9}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{2(-m^{-1})^{-4}}{9(m^{-3})^2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2(-1)^{-4}m^{-1(-4)}}{9m^{-3(2)}}
\\\\=
\dfrac{2(1)m^{4}}{9m^{-6}}
\\\\=
\dfrac{2m^{4-(-6)}}{9}
\\\\=
\dfrac{2m^{4+6}}{9}
\\\\=
\dfrac{2m^{10}}{9}
.\end{array}