Answer
$15\sqrt[3]{3}$
Work Step by Step
We simplify by using the fact that $\sqrt[n]{a}=a^{1/n}$ and then combine the like terms as follows:
$$
9\sqrt[3]{24}-\sqrt[3]{81}=9\sqrt[3]{3\times 2^3}-\sqrt[3]{3\times3^3}=18\sqrt[3]{3}-3\sqrt[3]{3}\\
=(18-3)\sqrt[3]{3}=15\sqrt[3]{3}
.$$
