# How do you simplify (\frac { x ^ { 2} y ^ { - 1} } { 2x ^ { 4} y ^ { 4} } ) ^ { 3}?

Sep 25, 2017

$\frac{1}{8 {x}^{6} {y}^{5}}$

#### Explanation:

Simplify inside the bracket first.

${\left(\frac{\textcolor{b l u e}{{x}^{2}} \textcolor{red}{{y}^{-} 1}}{2 \textcolor{b l u e}{{x}^{4}} {y}^{4}}\right)}^{3}$

$= {\left(\frac{1}{2 \textcolor{b l u e}{{x}^{2}} {y}^{4} \textcolor{red}{{y}^{1}}}\right)}^{3}$

$= {\left(\frac{1}{2 {x}^{2} {y}^{5}}\right)}^{3}$

$= \frac{1}{8 {x}^{6} {y}^{5}}$

Laws of indices:

To Divide: subtract indices of like bases: ${x}^{2} / {x}^{4} = \frac{1}{x} ^ \left(4 - 2\right) = \frac{1}{x} ^ 2$

${y}^{-} 1 = \frac{1}{y}$

To multiply, add indices of like bases: ${y}^{4} \times {y}^{1} = {y}^{5}$

Raising a power to a power, multiply the indices

${\left({x}^{2}\right)}^{3} = {x}^{2 \times 3} = {x}^{6}$