To apply the property of negative integer exponents, we can rewrite the expression \( 7^{-3} \cdot 7^{-5} \) using the property which states that \( a^{-n} = \frac{1}{a^n} \).
First, we can combine the two exponents:
\[ 7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8} \]
Now, using the property of negative exponents:
\[ 7^{-8} = \frac{1}{7^8} \]
Therefore, the expression \( 7^{-3} \cdot 7^{-5} \) can be rewritten with positive exponents only as:
\[ \frac{1}{7^8} \]