Answer
$\dfrac{9}{a^{8}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{a^4}{3} \right)^{-2}
$, is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{3}{a^4} \right)^{2}
\\\\=
\dfrac{3^2}{a^{4(2)}}
\\\\=
\dfrac{9}{a^{8}}
.\end{array}