## College Algebra (11th Edition)

$\sqrt[3]{2}$
$\bf{\text{Solution Outline:}}$ 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}