To simplify the expression \(\frac{36\sqrt{39}}{9\sqrt{13}}\), we can break it down into simpler parts.
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First, simplify the coefficients (the numeric parts): \[ \frac{36}{9} = 4 \]
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Next, simplify the square roots. The given expression can be rewritten as: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \frac{\sqrt{39}}{\sqrt{13}} \]
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Now, we simplify \(\frac{\sqrt{39}}{\sqrt{13}}\) using the property of square roots: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]
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Therefore, we can combine the results: \[ 4 \cdot \sqrt{3} \]
Thus, the exact answer is: \[ \boxed{4\sqrt{3}} \]