Answer
$-\sqrt[3]{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
9\sqrt[3]{2}-5\sqrt[3]{16}
,$ simplifies to
\begin{array}{l}\require{cancel}
9\sqrt[3]{2}-5\sqrt[3]{8\cdot2}
\\\\=
9\sqrt[3]{2}-5\sqrt[3]{(2)^3\cdot2}
\\\\=
9\sqrt[3]{2}-5(2)\sqrt[3]{2}
\\\\=
9\sqrt[3]{2}-10\sqrt[3]{2}
\\\\=
-\sqrt[3]{2}
.\end{array}
