Answer
$\sqrt[4]{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[4]{\sqrt{25}}
,$ use the definition of rational exponents.
$\bf{\text{Solution Details:}}$
Since $\sqrt{25}=5,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[4]{5}
.\end{array}
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}
5^{\frac{1}{4}}
\\\\=
5^{1/4}
\\\\=
\sqrt[4]{5}
.\end{array}
