#### Answer

$xy^2z^{3}\sqrt[3]{x^2z}$

#### Work Step by Step

Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[3]{x^5y^6z^{10}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{x^3y^6z^{9}\cdot x^2z}
\\\\=
\sqrt[3]{(xy^2z^{3})^3\cdot x^2z}
\\\\=
xy^2z^{3}\sqrt[3]{x^2z}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.