Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 78: 40

$15\sqrt[3]{3}$

Using the properties of radicals that we know, we simplify: $\displaystyle 9\sqrt[3]{24}-\sqrt[3]{81}=9\sqrt[3]{8*3}-\sqrt[3]{27*3}=9\sqrt[3]{2^3*3}-\sqrt[3]{3^3*3}=9*2\sqrt[3]{3}-3\sqrt[3]{3}=18\sqrt[3]{3}-3\sqrt[3]{3}=15\sqrt[3]{3}$