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