Answer
$\frac{1}{x^{9}y^{4}}$
Work Step by Step
We are given the expression $\frac{x^{-7}y^{-2}}{x^{2}y^{2}}$.
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).
$\frac{x^{-7}y^{-2}}{x^{2}y^{2}}=x^{-7-2}\times y^{-2-2}=x^{-9}\times y^{-4}$
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).
$x^{-9}\times y^{-4}=\frac{1}{x^{9}y^{4}}$