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