Answer
$2$.
Work Step by Step
The given expression is
$=\sqrt[3]{-4}(\sqrt[3]{2}-\sqrt[3]{16})$
Factor as cube terms.
$=\sqrt[3]{-4}(\sqrt[3]{2}-\sqrt[3]{8\cdot 2})$
Use product property of square roots.
$=\sqrt[3]{-4}(\sqrt[3]{2}-\sqrt[3]{8}\cdot \sqrt[3]{2})$
Use $8=2^3$.
$=\sqrt[3]{-4}(\sqrt[3]{2}-\sqrt[3]{2^3}\cdot \sqrt[3]{2})$
Simplify.
$=\sqrt[3]{-4}(\sqrt[3]{2}-2\sqrt[3]{2})$
Use distributive property.
$=\sqrt[3]{-4}\cdot \sqrt[3]{2}(1-2)$
Subtract.
$=\sqrt[3]{-4}\cdot \sqrt[3]{2}(-1)$
Use product property of square roots.
$=\sqrt[3]{-4\cdot 2}(-1)$
Multiply.
$=\sqrt[3]{-8}(-1)$
Use $-8=(-2)^3$.
$=\sqrt[3]{(-2)^3}(-1)$
Simplify.
$=(-2)(-1)$
$=2$.
