Question

How do you simplify `root3(x+2) times root3((x+2)^7)`?

Answer 1

Use `root n Axxroot n B=root n (AxxB)`

Explanation:

`=root 3 ((x+2)xx(x+2)^7)=root 3 ((x+2)^8`

Now we work the other way around to regroup the `(x+2)`'s:
`=root 3 ((x+2)^3xx(x+2)^3xx(x+2)^2)`
`=root 3 ((x+2)^3)xxroot 3 ((x+2)^3)xxroot 3 ((x+2)^2)`

Take out the 3rd powers:
`=(x+2)xx(x+2)xxroot 3 ((x+2)^2)`
`=(x+2)^2*root 3 ((x+2)^2)`

Answer 2

`=(x+2)^2timesroot3((x+2)^2)`

Explanation:

`root3(x+2)timesroot3((x+2)^7)`

`=root3((x+2)(x+2)^7)`

`=root3((x+2)^8`

`=(x+2)^2timesroot3((x+2)^2)`