Question

select the expression that is equivalent to ( x^{4}y^{8}z^{-7} )
options: ( x^{4}y^{8}z^{7} ), ( \frac{x^{4}y^{8}}{z^{7}} ), ( \frac{y^{8}}{x^{4}z^{7}} ), ( \frac{x^{4}}{y^{8}z^{7}} )

Explanation:

Step1: Apply negative exponent rule

Recall $a^{-n}=\frac{1}{a^n}$, so $z^{-7}=\frac{1}{z^7}$.

Step2: Rewrite original expression

Substitute $z^{-7}$ into $x^4y^8z^{-7}$:
$x^4y^8 \cdot \frac{1}{z^7} = \frac{x^4y^8}{z^7}$

Answer:

$\boldsymbol{\frac{x^4y^8}{z^7}}$ (the second option)