Answer
$\dfrac{3\sqrt[3]{4}}{2}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{3}{\sqrt[3]{2}}
$ results to
\begin{array}{l}
\dfrac{3}{\sqrt[3]{2}}
\cdot
\dfrac{\sqrt[3]{4}}{\sqrt[3]{4}}
\\\\=
\dfrac{3\sqrt[3]{4}}{\sqrt[3]{8}}
\\\\=
\dfrac{3\sqrt[3]{4}}{2}
.\end{array}