Answer
$z^{3}$
Work Step by Step
We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer).
Therefore, $\frac{z^{-4}}{z^{-7}}=\frac{1}{z^{4}}\times z^{7}=\frac{z^{7}}{z^{4}}=z^{7-4}=z^{3}$.