How do you simplify (2x^-3y)/( 10y^-2)?

May 6, 2016

${y}^{3} / \left(5 {x}^{3}\right)$

Explanation:

We know that ${x}^{-} n = \frac{1}{x} ^ n$

Applying this property to the variables:

Method 1:

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

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

$= {y}^{3} / \left(5 {x}^{3}\right)$

Method 2:

We can write all the variables in the numerator as

$\frac{2 \times {x}^{-} 3 \times y \times {y}^{-} \left(- 2\right)}{10}$

$= \frac{{x}^{-} 3 \times y \times {y}^{2}}{5}$ $\textcolor{red}{\text{cancelling 2}}$

$= \frac{{x}^{-} 3 \times {y}^{3}}{5}$

$= {y}^{3} / \left(5 {x}^{3}\right)$