Answer
$18\sqrt[3]{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
2\sqrt[3]{54}+6\sqrt[3]{16}
,$ simplifies to
\begin{array}{l}\require{cancel}
2\sqrt[3]{27\cdot2}+6\sqrt[3]{8\cdot2}
\\\\=
2\sqrt[3]{(3)^3\cdot2}+6\sqrt[3]{(2)^3\cdot2}
\\\\=
2\cdot3\sqrt[3]{2}+6\cdot2\sqrt[3]{2}
\\\\=
6\sqrt[3]{2}+12\sqrt[3]{2}
\\\\=
18\sqrt[3]{2}
.\end{array}
