## Algebra: A Combined Approach (4th Edition)

$\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{m^{2}n^{3}}$
$\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}$ Rewrite this expression as $\dfrac{\sqrt[5]{32}}{\sqrt[5]{m^{6}n^{13}}}$ and simplify it: $\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}=\dfrac{\sqrt[5]{32}}{\sqrt[5]{m^{6}n^{13}}}=\dfrac{2}{mn^{2}\sqrt[5]{mn^{3}}}=...$ Multiply the fraction by $\dfrac{\sqrt[5]{m^{4}n^{2}}}{\sqrt[5]{m^{4}n^{2}}}$ and simplify: $...=\dfrac{2}{mn^{2}\sqrt[5]{mn^{3}}}\cdot\dfrac{\sqrt[5]{m^{4}n^{2}}}{\sqrt[5]{m^{4}n^{2}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{mn^{2}\sqrt[5]{m^{5}n^{5}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{mn^{2}(m)(n)}=...$ $...=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{m^{2}n^{3}}$