Answer
$\dfrac{\sqrt[3]{6}}{3}$
Work Step by Step
Rationalizing the denominator of the given expression, $
\sqrt[3]{\dfrac{2}{9}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{2}{9}\cdot\dfrac{3}{3}}
\\\\=
\sqrt[3]{\dfrac{6}{27}}
\\\\=
\dfrac{\sqrt[3]{6}}{\sqrt[3]{27}}
\\\\=
\dfrac{\sqrt[3]{6}}{\sqrt[3]{(3)^3}}
\\\\=
\dfrac{\sqrt[3]{6}}{3}
.\end{array}