#### Answer

$r^{25}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}