Answer
$\dfrac{4x^2}{9}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$, the expression $
\left( \dfrac{8x^3}{27} \right)^{2/3}
$ simplifies to
\begin{array}{l}
\left( \sqrt[3]{\dfrac{8x^3}{27}} \right)^2
\\\\=
\left( \dfrac{2x}{3} \right)^2
\\\\=
\dfrac{4x^2}{9}
.\end{array}
