Answer
$\dfrac{a^3}{64}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
(4a^{-1}b^0)^{-3}
\\\\=
4^{-3}a^{-1(-3)}
\\\\=
\dfrac{a^3}{4^{3}}
\\\\=
\dfrac{a^3}{64}
.\end{array}
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