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

2 Answers
Aug 30, 2016

Answer:

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

Answer:

#=(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)#