Answer
$5\sqrt[3]{2}-\sqrt[3]{10}$.
Work Step by Step
The given expression is
$=\sqrt[3]5(\sqrt[3]{50}-\sqrt[3]{2})$
Use the distributive property.
$=\sqrt[3]5(\sqrt[3]{50})-\sqrt[3]5(\sqrt[3]{2})$
Use product rule.
$=\sqrt[3]{5\cdot50}-\sqrt[3]{5\cdot2}$
Simplify.
$=\sqrt[3]{250}-\sqrt[3]{10}$
Factor as a perfect cube.
$=\sqrt[3]{5^3\cdot 2}-\sqrt[3]{10}$
Use product rule.
$=\sqrt[3]{5^3}\cdot \sqrt[3]{2}-\sqrt[3]{10}$
Simplify.
$=5\sqrt[3]{2}-\sqrt[3]{10}$.
