Answer
$2x^{}y^{2}\sqrt[6]{2x^5y}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\sqrt[]{2x^3y^3}\sqrt[3]{4xy^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[2(3)]{2^{1(3)}x^{3(3)}y^{3(3)}}\cdot\sqrt[3(2)]{4^{1(2)}x^{1(2)}y^{2(2)}}
\\\\=
\sqrt[6]{2^{3}x^{9}y^{9}}\cdot\sqrt[6]{4^{2}x^{2}y^{4}}
\\\\=
\sqrt[6]{8x^{9}y^{9}}\cdot\sqrt[6]{16x^{2}y^{4}}
\\\\=
\sqrt[6]{8x^{9}y^{9}(16x^{2}y^{4})}
\\\\=
\sqrt[6]{128x^{9+2}y^{9+4}}
\\\\=
\sqrt[6]{128x^{11}y^{13}}
\\\\=
\sqrt[6]{64x^{6}y^{12}\cdot2x^5y}
\\\\=
\sqrt[6]{(2x^{}y^{2})^6\cdot2x^5y}
\\\\=
2x^{}y^{2}\sqrt[6]{2x^5y}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
