#### Answer

$64$

#### Work Step by Step

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