Question

select the expression that is equivalent to
$x^{2}y^{5}z^{-2}$
options: (some options are partially shown, like $\frac{x^{2}y^{5}}{z^{2}}$, $\frac{y^{5}}{x^{2}z^{2}}$ and one with $z^{2}$)

Explanation:

Step1: Apply negative exponent rule

Recall the rule $a^{-n}=\frac{1}{a^n}$, so $z^{-2}=\frac{1}{z^2}$.

Step2: Rewrite original expression

Substitute $z^{-2}$ into the original term:
$x^2y^5z^{-2}=x^2y^5\cdot\frac{1}{z^2}=\frac{x^2y^5}{z^2}$

Answer:

$\boldsymbol{\frac{x^2y^5}{z^2}}$ (the second option shown)