## Intermediate Algebra (6th Edition)

$\frac{1}{13}$
We are given the expression $\frac{13^{-10}}{13^{-9}}$. To simplify, we can use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers). $\frac{13^{-10}}{13^{-9}}=13^{-10-(-9)}=13^{-1}$ To simplify this into a positive exponent, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer). Therefore, $13^{-1}=\frac{1}{13}$