## Intermediate Algebra (12th Edition)

$-2zt^2\sqrt[3]{2z^2t}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[3]{-16z^5t^7} ,$ 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]{-8z^3t^6\cdot 2z^2t} \\\\= \sqrt[3]{(-2zt^2)^3\cdot 2z^2t} \\\\= -2zt^2\sqrt[3]{2z^2t} .\end{array}