Answer
$\dfrac{2}{3m^{6}n^{4}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{8m^{-2}n^3}{12m^4n^7}
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{4}\cdot2m^{-2-4}n^{3-7}}{\cancel{4}\cdot3}
\\\\=
\dfrac{2m^{-6}n^{-4}}{3}
\\\\=
\dfrac{2}{3m^{6}n^{4}}
.\end{array}