Answer
$\dfrac{2}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt[3]{16}}{\sqrt[3]{54}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{8\cdot2}}{\sqrt[3]{27\cdot2}}
\\\\=
\dfrac{\sqrt[3]{(2)^3\cdot2}}{\sqrt[3]{(3)^3\cdot2}}
\\\\=
\dfrac{2\sqrt[3]{2}}{3\sqrt[3]{2}}
\\\\=
\dfrac{2\cancel{\sqrt[3]{2}}}{3\cancel{\sqrt[3]{2}}}
\\\\=
\dfrac{2}{3}
.\end{array}
