To apply the Property of Negative Integer Exponents, we first recall that for any non-zero number \( a \) and a negative exponent \( n \), the expression can be rewritten as:
\[ a^{-n} = \frac{1}{a^{n}} \]
Now, let's rewrite the expression \( 7^{-3} \cdot 7^{-5} \).
According to the property of exponents which states that \( a^m \cdot a^n = a^{m+n} \), we can combine the exponents since the bases are the same:
\[ 7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8} \]
Next, we convert this into an expression with positive exponents:
\[ 7^{-8} = \frac{1}{7^8} \]
So, the expression \( 7^{-3} \cdot 7^{-5} \) with positive exponents only is:
\[ \frac{1}{7^8} \]