Answer
$\frac{1}{x^{7}}$
Work Step by Step
We are given the expression $\frac{x^{-2}}{x^{5}}$.
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).
Therefore, $\frac{x^{-2}}{x^{5}}=x^{-2-5}=x^{-7}$.
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).
$x^{-7}=\frac{1}{x^{7}}$