# How do you simplify (3wy ^-2)/((w^-1y)^3)?

May 5, 2015

We know that color(blue)((ab)^m = a^m*b^m

The denominator ${\left({w}^{-} 1 y\right)}^{3} = {w}^{- 1 \cdot 3} {y}^{3} = {w}^{-} 3 {y}^{3}$

The expression can hence be written as $\frac{3 w {y}^{-} 2}{{w}^{-} 3 \cdot {y}^{3}}$

$= 3 \cdot \left(\frac{w}{w} ^ - 1\right) \cdot \left({y}^{-} \frac{2}{y} ^ 3\right)$

We also know that color(blue)(a^m/a^n = a^(m-n)

$= 3 \cdot {w}^{1 - \left(- 1\right)} \cdot {y}^{- 2 - 3}$

$= 3 \cdot {w}^{2} \cdot {y}^{-} 5$

 =color(green)( (3w^2)/y^5