Answer
$\dfrac{2a^2}{\sqrt[3]{28a^2b}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\sqrt[3]{\dfrac{2a^4}{7b}}
,$ is equivalent to
\begin{array}{l}
\sqrt[3]{\dfrac{2a^4}{7b}\cdot\dfrac{4a^2}{4a^2}}
\\\\=
\sqrt[3]{\dfrac{8a^6}{28a^2b}}
\\\\=
\sqrt[3]{\dfrac{(2a^2)^3}{28a^2b}}
\\\\=
\dfrac{2a^2}{\sqrt[3]{28a^2b}}
.\end{array}