#### Answer

$5\sqrt[3]{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{15}{\sqrt[3]{9}}
,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{15}{\sqrt[3]{3^2}}
\\\\=
\dfrac{15}{\sqrt[3]{3^2}}\cdot\dfrac{\sqrt[3]{3}}{\sqrt[3]{3}}
\\\\=
\dfrac{15\sqrt[3]{3}}{\sqrt[3]{3^2}(\sqrt[3]{3})}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\dfrac{15\sqrt[3]{3}}{\sqrt[3]{3^2(3)}}
\\\\=
\dfrac{15\sqrt[3]{3}}{\sqrt[3]{3^3}}
\\\\=
\dfrac{15\sqrt[3]{3}}{3}
\\\\=
\dfrac{\cancel{3}(5)\sqrt[3]{3}}{\cancel{3}}
\\\\=
5\sqrt[3]{3}
.\end{array}