Answer
$x^{2}y^{}z^{3}\sqrt[5]{x^3y^3z^2}$
Work Step by Step
Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[5]{x^{13}y^{8}z^{17}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{x^{10}y^{5}z^{15}\cdot x^3y^3z^2}
\\\\=
\sqrt[5]{(x^{2}y^{}z^{3})^5\cdot x^3y^3z^2}
\\\\=
x^{2}y^{}z^{3}\sqrt[5]{x^3y^3z^2}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.