To simplify the expression \( 7^{-3} \cdot 7^{-5} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this property:
\[ 7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8} \]
So, the simplified result is:
\[ 7^{-8} \]
If you want to express \( 7^{-8} \) as a positive exponent, you can write:
\[ 7^{-8} = \frac{1}{7^8} \]
Thus, the final answer can be written as either \( 7^{-8} \) or \( \frac{1}{7^8} \).