Answer
$15\sqrt[3]{3}$
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a perfect cube:
$9\sqrt[3]{24}-\sqrt[3]{81}\\
=9\sqrt[3]{8\cdot 3}-\sqrt[3]{27\cdot 3}\\
=9\sqrt[3]{2^3\cdot 3}-\sqrt[3]{3^3\cdot 3}\\$
Use the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}$ then simplify:
$=9\sqrt[3]{2^3}\cdot\sqrt[3]{3} -\sqrt[3]{3^3}\cdot \sqrt[3]{3}$
$=9\cdot2\cdot\sqrt[3]{3} -3\cdot \sqrt[3]{3}$
$=18\sqrt[3]{3} -3\sqrt[3]{3}$
Factor out $\sqrt[3]{3}$ then simplify.
$=\sqrt[3]{3}(18-3)$
$=\sqrt[3]{3}(15)$
$=15\sqrt[3]{3}$
Hence, the correct answer is $15\sqrt[3]{3}$.
