Question

How do you simplify `(x^5y^8)/(x^4y^2)`?

Answer 1

The answer is `xy^6`

Let's see how we get there.

First the long way. You can write `y^2` as `y*y` etc.

Your formula then is:

`(x*x*x*x*x*y*y*y*y*y*y*y*y)/(x*x*x*x*y*y)`

Now cross out the `x`'s and `y`'s above and below the dividing bar two by two. You will be left with:

`x*y*y*y*y*y*y` and nothing below the bar

This can be written as `x*y^6=xy^6`

A shorter way would be to subtract the exponents:

First we rewrite: `(x^5*y^8)/(x^4*y^2)=x^5/x^4*y^8/y^2`

`x^5/x^4=x^(5-4)=x^1=x` and `y^8/y^2=y^(8-2)=y^6`

Answer: `x*y^6=xy^6` (same answer of course)