Question

select the expression that is equivalent to \\(\frac{1}{x^{6}y^{-9}z^{-1}}\\)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$, so $y^{-9}=\frac{1}{y^9}$, $z^{-1}=\frac{1}{z}$. Substitute into denominator:
$\frac{1}{x^6 \cdot \frac{1}{y^9} \cdot \frac{1}{z}}$

Step2: Simplify the denominator

Multiply the terms in the denominator:
$\frac{1}{\frac{x^6}{y^9 z}}$

Step3: Invert denominator to simplify

Dividing by a fraction is multiplying by its reciprocal:
$1 \cdot \frac{y^9 z}{x^6} = \frac{y^9 z}{x^6}$
(Note: This can also be written as $\frac{y^9}{x^6 z}$ which matches the first option)

Answer:

$\frac{y^9}{x^6 z}$