To divide \( 36\sqrt{39} \) by \( 9\sqrt{13} \), we can rewrite it mathematically as:
\[ \frac{36\sqrt{39}}{9\sqrt{13}} \]
Now we can simplify this fraction.
- Divide the coefficients (the numbers outside the square roots), which are \( 36 \) and \( 9 \):
\[ \frac{36}{9} = 4 \]
- Now take the square roots:
\[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]
Now, we can combine the simplified parts:
\[ 4 \cdot \sqrt{3} = 4\sqrt{3} \]
Therefore, the exact answer is:
\[ \boxed{4\sqrt{3}} \]
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