#### Answer

$5^{-9}$

#### Work Step by Step

We are given the numbers $5^{-10}$ and $5^{-9}$. We know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).
Without calculating completely, we know that $5^{-10}=\frac{1}{5^{10}}=\frac{1}{5^{9}\times5^{1}}$.
Therefore, both numbers will have the same numerator, but $5^{-10}$ will have a denominator that is $5^{1}=5$ times greater than the denominator of $5^{-9}$. So, we know that $5^{-9}$ will be a larger number.