Question

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

Answer 1

`(2y)/(2x^(-1)y^(-1)) = xy^2`

Explanation:

Consider these examples:

`1/x " is another way of writing " x^(-1)`

`x^(-1)" " ->" " x^(-1)/1 " is another way of writing " 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:`" "(2y)/(2x^(-1)y^(-1))`

`color(saddlebrown)(2xx1/2)color(green)(xxy)color(blue)(xx1/x^(-1))color(magenta)(xx1/y^(-1))`

`color(saddlebrown)(2/2)color(green)(xxy)color(blue)(xx1/x^(-1))color(magenta)(xx1/y^(-1))`

Note that `2/2=1` so this gives:

`color(saddlebrown)(1) color(green)(xxy)color(blue)(xx x)color(magenta)(xxy)`

`xy^2`