Answer
$-\sqrt[3]{2}$
Work Step by Step
Simplify the second radical by factoring the radicand such that one of the factors is a perfect cube:
$5\sqrt[3]{2}-2\sqrt[3]{54}\\
=5\sqrt[3]{2}-2\sqrt[3]{27\cdot 2}\\
=5\sqrt[3]{2}-2\sqrt[3]{3^3\cdot 2}$
Use the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}$ then simplify:
$=5\sqrt[3]{2}-2\sqrt[3]{3^3}\cdot \sqrt[3]{2}$
$=5\sqrt[3]{2}-2\cdot3\cdot \sqrt[3]{2}$
$=5\sqrt[3]{2}-6\sqrt[3]{2}$
Factor out $\sqrt[3]{2}$ then simplify.
$=\sqrt[3]{2}(5-6)$
$=\sqrt[3]{2}(-1)$
$=-\sqrt[3]{2}$
Hence, the correct answer is $-\sqrt[3]{2}$.
