## Intermediate Algebra (12th Edition)

$64$
$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $\sqrt[3]{4^{9}} ,$ 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} 4^{\frac{9}{3}} \\\\= 4^{3} \\\\= 64 .\end{array}