To simplify the expression \( 7^{-3} \times 7^{-5} \) using the property of negative integer exponents, we first use the rule that states:
\[ a^{-m} \times a^{-n} = a^{-(m+n)} \]
Applying this rule:
\[ 7^{-3} \times 7^{-5} = 7^{-(3+5)} = 7^{-8} \]
Now, to express \( 7^{-8} \) with a positive exponent, we can use the property that states:
\[ a^{-m} = \frac{1}{a^m} \]
Thus,
\[ 7^{-8} = \frac{1}{7^8} \]
Therefore, the expression \( 7^{-3} \times 7^{-5} \) with positive exponents only is:
\[ \frac{1}{7^8} \]
So, filling in the blank:
\[ 7^{-3} \times 7^{-5} = \frac{1}{7^8} \]