Answer
$\dfrac{a^8}{b^{24}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(a^{-2}b^6)^{-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
a^{-2(-4)}b^{6(-4)}
\\\\=
a^{8}b^{-24}
\\\\=
\dfrac{a^8}{b^{24}}
.\end{array}