Question

select the expression that is equivalent to
\\(\frac{1}{x^{-4}y^{2}z^{2}}\\)
options:
\\(\frac{x^{4}y^{2}}{z^{2}}\\), \\(\frac{1}{x^{4}y^{2}z^{2}}\\), \\(\frac{x^{4}z^{2}}{y^{2}}\\), \\(\frac{x^{4}}{y^{2}z^{2}}\\)

Explanation:

Step1: Rewrite negative exponent

Recall $x^{-n}=\frac{1}{x^n}$, so $x^{-4}=\frac{1}{x^4}$. Substitute into denominator:
$\frac{1}{\frac{1}{x^4}y^2z^2}$

Step2: Simplify complex fraction

Dividing by a fraction is multiplying by its reciprocal:
$1 \times \frac{x^4}{y^2z^2} = \frac{x^4}{y^2z^2}$

Answer:

$\boldsymbol{\frac{x^4}{y^2z^2}}$ (the fourth option)