#### Answer

$x^{}y^{3}\sqrt[3]{xy}$

#### Work Step by Step

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