## College Algebra (11th Edition)

$2x^2z^4\sqrt{2x}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt{8x^5z^8} ,$ use the laws of exponents to simplify the radicand. Then, find a factor of the radicand that is a perfect power of the index. Finally, extract the root of the factor that is a perfect power of the root. $\bf{\text{Solution Details:}}$ Factoring the expression that is a perfect power of the index and then extracting the root result to \begin{array}{l}\require{cancel} \sqrt{4x^4z^8\cdot2x} \\\\= \sqrt{(2x^2z^4)^2\cdot2x} \\\\= |2x^2z^4|\sqrt{2x} .\end{array} Since all variables are assumed to be positive, then, \begin{array}{l}\require{cancel} 2x^2z^4\sqrt{2x} .\end{array}