# How do you simplify (y ^ { 3} z ^ { - 1} ) ( \frac { x y ^ { - 2} } { 3z ^ { - 2} } ) ^ { 2}?

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#### Explanation

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#### Explanation:

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Feb 6, 2018

$= \frac{{x}^{2} {z}^{3}}{9 y}$

#### Explanation:

Simplify:
$\left({y}^{3} {z}^{-} 1\right) {\left(\frac{x {y}^{-} 2}{3 {z}^{-} 2}\right)}^{2}$
$= {y}^{3} \left(\frac{1}{z}\right) {\left(x {y}^{-} 2\right)}^{2} / {\left(3 {z}^{-} 2\right)}^{2}$
$= {y}^{3} / z \frac{{x}^{2} {y}^{-} 4}{{3}^{2} {z}^{-} 4}$
$= \frac{{y}^{3 - 4} {x}^{2}}{9 {z}^{1 - 4}}$
$= \frac{{y}^{-} 1 {x}^{2}}{9 {z}^{-} 3}$
$= \frac{1}{y} \left(\frac{1}{9}\right) {x}^{2} {z}^{3}$
$= \frac{{x}^{2} {z}^{3}}{9 y}$

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