#### Answer

$25\sqrt[3]{a^2}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(125a)^{2/3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{(125a)^2}
\\\\=
\left( \sqrt[3]{125a} \right)^2
\\\\=
\left( \sqrt[3]{(5)^3a} \right)^2
\\\\=
\left( 5\sqrt[3]{a} \right)^2
\\\\=
5^2\sqrt[3]{a^2}
\\\\=
25\sqrt[3]{a^2}
.\end{array}