Answer
$\dfrac{27b^{12}}{8a^{6}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{2a^2}{3b^4} \right)^{-3}
$, is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{3b^4}{2a^2} \right)^{3}
\\\\=
\dfrac{3^3b^{4(3)}}{2^3a^{2(3)}}
\\\\=
\dfrac{27b^{12}}{8a^{6}}
.\end{array}