To simplify the expression \( 5^{-9} \times 5^{-8} \), you can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Applying this property:
\[ 5^{-9} \times 5^{-8} = 5^{-9 + (-8)} = 5^{-17} \]
So, the simplified expression is:
\[ 5^{-17} \]
If you want to express it in terms of positive exponents, you can write it as:
\[ \frac{1}{5^{17}} \]