Answer
$\sqrt[3]{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[3]{\sqrt{4}}
,$ use the definition of rational exponents.
$\bf{\text{Solution Details:}}$
Since $\sqrt{4}=2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{2}
.\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}
2^{\frac{1}{3}}
\\\\=
2^{1/3}
\\\\=
\sqrt[3]{2}
.\end{array}
