Intermediate Algebra (12th Edition)

$x^3y^4\sqrt[]{13x}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[]{13x^7y^8} ,$ 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 results to \begin{array}{l}\require{cancel} \sqrt[]{x^6y^8\cdot13x} \\\\= \sqrt[]{(x^3y^4)^2\cdot13x} \\\\= x^3y^4\sqrt[]{13x} .\end{array}