## Intermediate Algebra (6th Edition)

$\frac{1}{z^{3}}$
We are given the expression $\frac{z^{12}}{z^{15}}$. We can use the quotient rule to simplify this expression. $\frac{z^{12}}{z^{15}}=z^{12-15}=z^{-3}$ We know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer). Therefore, $z^{-3}=\frac{1}{z^{3}}$