Answer
$\dfrac{32d^{15}}{a^{10}b^5}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{a^2b}{2d^3} \right)^{-5}
$, is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{2d^3}{a^2b} \right)^{5}
\\\\=
\dfrac{2^5d^{3(5)}}{a^{2(5)}b^5}
\\\\=
\dfrac{32d^{15}}{a^{10}b^5}
.\end{array}