Answer
$\dfrac{9q^{8}}{4p^{6}}$
Work Step by Step
In order to simplify the expression, we distribute the -2 into the parenthesis. Using the laws of exponents, the given expression, $
\left( \dfrac{2p^3}{3q^4} \right)^{-2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2^{1(-2)}p^{3(-2)}}{3^{1(-2)}q^{4(-2)}}
\\\\=
\dfrac{2^{-2}p^{-6}}{3^{-2}q^{-8}}
\\\\=
\dfrac{3^{2}q^{8}}{2^{2}p^{6}}
\\\\=
\dfrac{9q^{8}}{4p^{6}}
.\end{array}
