Answer
$\dfrac{1}{a^{12}b^{15}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(a^4b^5)^{-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
a^{4(-3)}b^{5(-3)}
\\\\=
a^{-12}b^{-15}
\\\\=
\dfrac{1}{a^{12}b^{15}}
.\end{array}