## Intermediate Algebra (12th Edition)

$\dfrac{v^{6}\sqrt[]{v}}{7}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[]{\dfrac{v^{13}}{49}} ,$ 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[]{\dfrac{v^{12}}{49}\cdot v} \\\\= \sqrt[]{\left( \dfrac{v^{6}}{7} \right)^2\cdot v} \\\\= \dfrac{v^{6}}{7}\sqrt[]{v} \\\\= \dfrac{v^{6}\sqrt[]{v}}{7} .\end{array}