#### Answer

$x^{}y^{}z^{}\sqrt[6]{x^5yz^2}$

#### Work Step by Step

Using the same indices for the radicals, the given expression, $
\sqrt[3]{xy^2z}\sqrt[]{x^3yz^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3(2)]{x^{1(2)}y^{2(2)}z^{1(2)}}\cdot\sqrt[2(3)]{x^{3(3)}y^{1(3)}z^{2(3)}}
\\\\=
\sqrt[6]{x^{2}y^{4}z^{2}}\cdot\sqrt[6]{x^{9}y^{3}z^{6}}
\\\\=
\sqrt[6]{x^{2}y^{4}z^{2}(x^{9}y^{3}z^{6})}
\\\\=
\sqrt[6]{x^{2+9}y^{4+3}z^{2+6}}
\\\\=
\sqrt[6]{x^{11}y^{7}z^{8}}
\\\\=
\sqrt[6]{x^{6}y^{6}z^{6}\cdot x^5yz^2}
\\\\=
\sqrt[6]{(x^{}y^{}z^{})^6\cdot x^5yz^2}
\\\\=
x^{}y^{}z^{}\sqrt[6]{x^5yz^2}
\end{array}
* Note that it is assumed that all variables represent positive numbers.