To divide \( 36\sqrt{39} \) by \( 9\sqrt{13} \), we follow these steps:
\[ \frac{36\sqrt{39}}{9\sqrt{13}} \]
First, we can simplify the coefficients (the numbers outside the square roots):
\[ \frac{36}{9} = 4 \]
Next, we can rewrite the expression:
\[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \frac{\sqrt{39}}{\sqrt{13}} \]
Now, we can simplify \( \frac{\sqrt{39}}{\sqrt{13}} \) as follows:
\[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]
Now we can combine the results:
\[ 4 \cdot \sqrt{3} \]
Thus, the exact answer is:
\[ \boxed{4\sqrt{3}} \]