To simplify the expression \(\frac{36\sqrt{39}}{9\sqrt{13}}\), we can follow these steps:
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Simplify the coefficients: \[ \frac{36}{9} = 4 \]
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Rewrite the expression: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \frac{\sqrt{39}}{\sqrt{13}} \]
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Simplify the square root part: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]
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Combine the results: \[ 4 \cdot \sqrt{3} = 4\sqrt{3} \]
Therefore, the simplified expression is: \[ \boxed{4\sqrt{3}} \]