Answer
$-\sqrt[3]{10}$
Work Step by Step
The given expression is
$=\sqrt[3]{2}(\sqrt[3]{135}-4\sqrt[3]{5})$
Factor as cube term.
$=\sqrt[3]{2}(\sqrt[3]{27\cdot 5}-4\sqrt[3]{5})$
Use product property of cube roots.
$=\sqrt[3]{2}(\sqrt[3]{27}\cdot \sqrt[3]{5}-4\sqrt[3]{5})$
Simplify.
$=\sqrt[3]{2}(3 \sqrt[3]{5}-4\sqrt[3]{5})$
Factor out $\sqrt[3]{5}$.
$=\sqrt[3]{2}\sqrt[3]{5}(3-4)$
Simplify.
$=\sqrt[3]{2}\sqrt[3]{5}(-1)$
Use product property of cube roots.
$=-\sqrt[3]{2\cdot 5}$
$=-\sqrt[3]{10}$