Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 8

$2\sqrt[3] 3$

$\frac{6}{\sqrt[3] 9}=\frac{6 \times \sqrt[3] (9^{2}) }{\sqrt[3] 9 \times \sqrt[3] (9^{2})}=\frac{6\times\sqrt[3] (9^{2}) }{\sqrt[3] (9\times9^{2})}=\frac{6\sqrt[3] (9^{2}) }{\sqrt[3] (9^{3})}$ $=\frac{6\sqrt[3] 81}{9}=\frac{6\sqrt[3] (27\times3)}{9}=\frac{(6\times3)\sqrt[3] 3}{9}=\frac{18\sqrt[3] 3}{9}=2\sqrt[3] 3$ We know that $\sqrt[3] 27=3$, because $3^{3}=27$.