Answer
$\dfrac{1}{81x^{20}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{6x^7}{2x^2} \right)^{-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( (6\div2)x^{7-2} \right)^{-4}
\\\\=
\left( 3x^{5} \right)^{-4}
\\\\=
3^{1(-4)}x^{5(-4)}
\\\\=
3^{-4}x^{-20}
\\\\=
\dfrac{1}{3^{4}x^{20}}
\\\\=
\dfrac{1}{81x^{20}}
.\end{array}