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

2 Answers
Aug 30, 2016

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)

Aug 30, 2016

=(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)