Answer
$s^{2}t^{3}\sqrt[3]{t}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{s^2t^4}\sqrt[3]{s^4t^6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{s^2t^4(s^4t^6)}
\\\\=
\sqrt[3]{s^{2+4}t^{4+6}}
\\\\=
\sqrt[3]{s^{6}t^{10}}
\\\\=
\sqrt[3]{s^{6}t^{9}\cdot t}
\\\\=
\sqrt[3]{(s^{2}t^{3})^3\cdot t}
\\\\=
s^{2}t^{3}\sqrt[3]{t}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.