## Intermediate Algebra (6th Edition)

$z^{5x-7}$
We are given the expression $\frac{z^{5x}\times z^{x-7}}{z^{x}}$. To simplify the numerator we can use the product rule, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). $\frac{z^{5x}\times z^{x-7}}{z^{x}}=\frac{z^{5x+x-7}}{z^{x}}=\frac{z^{6x-7}}{z^{x}}$ Next, we can use the quotient rule to simplify, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers). $\frac{z^{6x-7}}{z^{x}}=z^{6x-7-x}=z^{5x-7}$