Answer
$\frac{b^{10}}{a^{3}}$
Work Step by Step
We are given the expression $\frac{a^{-5}b^{7}}{a^{-2}b^{-3}}$.
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).
$\frac{a^{-5}b^{7}}{a^{-2}b^{-3}}=a^{-5-(-2)}\times b^{7-(-3)}=a^{-3}\times b^{10}$
To simplify this into only positive exponents, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).
$a^{-3}\times b^{10}=\frac{b^{10}}{a^{3}}$