Question

select the expression that is equivalent to
\\(\frac{x^{-5}y^{-2}}{z^{-7}}\\)
options:
\\(\frac{1}{x^5y^2z^7}\\)
\\(\frac{y^2z^7}{x^5}\\)
\\(\frac{z^7}{x^5y^2}\\)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$, so:
$\frac{x^{-5}y^{-2}}{z^{-7}} = \frac{\frac{1}{x^5} \cdot \frac{1}{y^2}}{\frac{1}{z^7}}$

Step2: Simplify the complex fraction

Dividing by a fraction is multiplying by its reciprocal:
$\frac{\frac{1}{x^5 y^2}}{\frac{1}{z^7}} = \frac{1}{x^5 y^2} \cdot z^7 = \frac{z^7}{x^5 y^2}$

Answer:

$\boldsymbol{\frac{z^7}{x^5 y^2}}$ (matches the third option shown)