To divide \( \frac{9\sqrt{33}}{27\sqrt{11}} \), we start by simplifying the fraction.
First, simplify the numerical coefficients:
\[ \frac{9}{27} = \frac{1}{3} \]
Next, simplify the square root part:
\[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} \]
Calculating \( \frac{33}{11} \):
\[ \frac{33}{11} = 3 \]
Then we have:
\[ \sqrt{\frac{33}{11}} = \sqrt{3} \]
Now, we can combine the results:
\[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3} \cdot \sqrt{3} = \frac{\sqrt{3}}{3} \]
Thus, the exact answer is:
\[ \frac{\sqrt{3}}{3} \]