#### Answer

$625$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
125^{4/3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{125^4}
\\\\=
\left( \sqrt[3]{125} \right)^4
\\\\=
\left( \sqrt[3]{(5)^3} \right)^4
\\\\=
\left( 5 \right)^4
\\\\=
625
.\end{array}