Answer
$\dfrac{x^{20}}{64y^{14}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{8x^{-6}y^3}{x^4y^{-4}} \right)^{-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{8^{-2}x^{-6(-2)}y^{3(-2)}}{x^{4(-2)}y^{-4(-2)}}
\\\\=
\dfrac{8^{-2}x^{12}y^{-6}}{x^{-8}y^{8}}
\\\\=
8^{-2}x^{12-(-8)}y^{-6-8}
\\\\=
8^{-2}x^{12+8}y^{-6-8}
\\\\=
8^{-2}x^{20}y^{-14}
\\\\=
\dfrac{x^{20}}{8^{2}y^{14}}
\\\\=
\dfrac{x^{20}}{64y^{14}}
.\end{array}
