## Intermediate Algebra (12th Edition)

$-3mn^{3}\sqrt[3]{3mn}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[3]{-81m^4n^{10}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index and then extracting the root of that factor results to \begin{array}{l}\require{cancel} \sqrt[3]{-27m^3n^{9}\cdot3mn} \\\\= \sqrt[3]{(-3mn^{3})^3\cdot3mn} \\\\= -3mn^{3}\sqrt[3]{3mn} .\end{array}