Answer
$\frac{1}{z^{22}}$
Work Step by Step
We are given the expression $\frac{z^{-12}}{z^{10}}$.
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, $\frac{z^{-12}}{z^{10}}=z^{-12-10}=z^{-22}$.
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).
$z^{-22}=\frac{1}{z^{22}}$