Answer
$\dfrac{b^{4}}{16a^{12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(2a^3b^{-1})^{-4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
2^{-4}a^{3(-4)}b^{-1(-4)}
\\\\=
2^{-4}a^{-12}b^{4}
\\\\=
\dfrac{b^{4}}{2^{4}a^{12}}
\\\\=
\dfrac{b^{4}}{16a^{12}}
.\end{array}
