Answer
$-8\sqrt[3]{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
2\sqrt[3]{24}-4\sqrt[3]{81}
,$ simplifies to
\begin{array}{l}\require{cancel}
2\sqrt[3]{8\cdot3}-4\sqrt[3]{27\cdot3}
\\\\=
2\sqrt[3]{(2)^3\cdot3}-4\sqrt[3]{(3)^3\cdot3}
\\\\=
2\cdot2\sqrt[3]{3}-4\cdot3\sqrt[3]{3}
\\\\=
4\sqrt[3]{3}-12\sqrt[3]{3}
\\\\=
-8\sqrt[3]{3}
.\end{array}
