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

Nov 23, 2016

$\frac{2 y}{2 {x}^{- 1} {y}^{- 1}} = x {y}^{2}$

#### Explanation:

Consider these examples:

$\frac{1}{x} \text{ is another way of writing } {x}^{- 1}$

${x}^{- 1} \text{ " ->" " x^(-1)/1 " is another way of writing } \frac{1}{x}$
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Using the above approach

Splitting up the given expression so you can see more of what is going on. So we have:

Given:$\text{ } \frac{2 y}{2 {x}^{- 1} {y}^{- 1}}$

$\textcolor{s a \mathrm{dd} \le b r o w n}{2 \times \frac{1}{2}} \textcolor{g r e e n}{\times y} \textcolor{b l u e}{\times \frac{1}{x} ^ \left(- 1\right)} \textcolor{m a \ge n t a}{\times \frac{1}{y} ^ \left(- 1\right)}$

$\textcolor{s a \mathrm{dd} \le b r o w n}{\frac{2}{2}} \textcolor{g r e e n}{\times y} \textcolor{b l u e}{\times \frac{1}{x} ^ \left(- 1\right)} \textcolor{m a \ge n t a}{\times \frac{1}{y} ^ \left(- 1\right)}$

Note that $\frac{2}{2} = 1$ so this gives:

$\textcolor{s a \mathrm{dd} \le b r o w n}{1} \textcolor{g r e e n}{\times y} \textcolor{b l u e}{\times x} \textcolor{m a \ge n t a}{\times y}$

$x {y}^{2}$