## Intermediate Algebra (12th Edition)

$r^{25}$
$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $\sqrt[]{r^{50}} ,$ to exponential form. $\bf{\text{Solution Details:}}$ Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[2]{r^{50}} \\\\= r^{\frac{50}{2}} \\\\= r^{25} .\end{array}