Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x^{2}y^{}z^{3}\sqrt[5]{x^3y^3z^2}$
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.