To simplify the expression \( 3^{9} \cdot 3^{-5} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this property here:
\[ 3^{9} \cdot 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^{4} \]
Now, we can calculate \( 3^{4} \):
\[ 3^{4} = 3 \cdot 3 \cdot 3 \cdot 3 = 81 \]
Thus, the numerical equivalent of \( 3^{9} \cdot 3^{-5} \) is \( \boxed{81} \).
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