Question

select the expression that is equivalent to
\\(\frac{y^{-5}}{x^{-4}z^{-2}}\\)
options:
\\(\frac{x^4 z^2}{y^5}\\)
\\(\frac{z^2}{x^4 y^5}\\)
\\(x^4 y^5 z^2\\)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$ and $\frac{1}{a^{-n}}=a^n$. So:
$\frac{y^{-5}}{x^{-4}z^{-2}} = y^{-5} \cdot \frac{1}{x^{-4}} \cdot \frac{1}{z^{-2}} = \frac{1}{y^5} \cdot x^4 \cdot z^2$

Step2: Combine terms

Multiply the positive exponents and the fraction:
$\frac{x^4 z^2}{y^5}$

Answer:

$\frac{x^4 z^2}{y^5}$ (the first option)