To find the numerical equivalent of \(3^9 \cdot 3^{-5}\), we can apply the laws of exponents. Specifically, when multiplying powers with the same base, we add the exponents:
\[ 3^9 \cdot 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^4 \]
Now, we just need to calculate \(3^4\):
\[ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 9 \cdot 9 = 81 \]
Thus, the numerical equivalent of \(3^9 \cdot 3^{-5}\) is \(\boxed{81}\).
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