Answer
$\dfrac{1}{96m^{7}} $
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{6m^{-4}}{m^{-9}} \right)^{-1}\left(\dfrac{m^{-2}}{16}\right)
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( \dfrac{m^{-9}}{6m^{-4}} \right)^{1}\left(\dfrac{m^{-2}}{16}\right)
\\\\=
\dfrac{m^{-9}m^{-2}}{6(16)m^{-4}}
\\\\=
\dfrac{m^{-9+(-2)-(-4)}}{96}
\\\\=
\dfrac{m^{-9-2+4}}{96}
\\\\=
\dfrac{m^{-7}}{96}
\\\\=
\dfrac{1}{96m^{7}}
.\end{array}
