Answer
$9\sqrt[3]{2}$
Work Step by Step
Simplifying each term and then combining like terms, the given expression, $
3\sqrt[3]{16}+\sqrt[3]{54}
,$ is equivalent to
\begin{array}{l}\require{cancel}
3\sqrt[3]{8\cdot2}+\sqrt[3]{27\cdot2}
\\\\=
3\sqrt[3]{(2)^3\cdot2}+\sqrt[3]{(3)^3\cdot2}
\\\\=
3\cdot2\sqrt[3]{2}+3\sqrt[3]{2}
\\\\=
6\sqrt[3]{2}+3\sqrt[3]{2}
\\\\=
9\sqrt[3]{2}
.\end{array}