Question

How do you simplify `\frac{3x^{2} y^{2}}{4x y^{4}}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`3/4(x^2/x)(y^2/y^4)`

Next, use these three rules of exponents to begin the simplification process:

`a = a^color(blue)(1)` and `x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `x^color(green)(a)/x^color(purple)(b) = 1/x^(color(purple)(b)-color(green)(a))`

`3/4(x^2/x)(y^2/y^4) = 3/4(x^color(red)(2)/x^color(blue)(1))(y^color(green)(2)/y^color(purple)(4)) = 3/4(x^(color(red)(2)-color(blue)(1)))(1/y^(color(purple)(4)-color(green)(2))) =`

`3/4(x^1)(1/y^2) = (3x^1)/(4y^2)`

Now, use this rule of exponents (the reverse of the first rule used above) to complete the simplification:

`a^color(red)(1) = a`

`(3x^color(red)(1))/(4y^2) = (3x)/(4y^2)`

Answer 2

`(3x)/(4y^2)`

Explanation:

`color(blue)((3x^2y^2)/(4xy^4)`

Cancel the variables

`rarr(3cancel(x^2)y^2)/(4cancelxy^4)`

`rarr(3xy^2)/(4y^4)`

`rarr(3xcancel(y^2))/(4cancel(y^4)`

`color(green)(rArr(3x)/(4y^2)`

Hope this helps!.. :)