#### Answer

$r^{\frac{3}{2}}$

#### Work Step by Step

We are given that $(\sqrt[n] a)^{m}=\sqrt[n] a^{m}=a^{\frac{m}{n}}$, as long as all indicated roots are real numbers.
Therefore, $\sqrt[6] r^{9}=r^{\frac{9}{6}}=r^{\frac{9\div3}{6\div3}}=r^{\frac{3}{2}}$.