Answer
$\dfrac{3}{7\sqrt[3]{3}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the numerator of the given expression, $
\dfrac{\sqrt[3]{9}}{7}
,$ multiply by an expression equal to $1$ which will make the numerator a perfect power of the index. Then extract the root of the factor that is a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the given expression by an expression equal to $1$ which will make the numerator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{9}}{7}\cdot\dfrac{\sqrt[3]{3}}{\sqrt[3]{3}}
\\\\=
\dfrac{\sqrt[3]{27}}{7\sqrt[3]{3}}
\\\\=
\dfrac{\sqrt[3]{(3)^3}}{7\sqrt[3]{3}}
\\\\=
\dfrac{3}{7\sqrt[3]{3}}
.\end{array}
