## Intermediate Algebra (12th Edition)

$2abc^3\sqrt[3]{b^2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\sqrt[3]{8a^3b^5c^9} ,$ write the radicand as an expression that contains a factor that is a perfect power of the index. Then extract the root of that factor. $\bf{\text{Solution Details:}}$ Writing the radicand as an expression that contains a factor that is a perfect power of the index and extracting the root of that factor result to \begin{array}{l}\require{cancel} \sqrt[3]{8a^3b^3c^9\cdot b^2} \\\\= \sqrt[3]{(2abc^3)^3\cdot b^2} \\\\= 2abc^3\sqrt[3]{b^2} .\end{array}