Homework Help

What is the simplest form of the expression ∛128a^13b^6

user profile pic

connorcolin3 | (Level 1) Valedictorian

Posted December 31, 2012 at 6:40 PM via web

dislike 2 like

What is the simplest form of the expression

∛128a^13b^6

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted December 31, 2012 at 7:07 PM (Answer #1)

dislike 1 like

Simplify `root(3)(128a^(13)b^(6))` :

A radical expression is simplified if there are no fractions in the radicand, no radicals in the denominator, and no perfect nth power factors in the radicand.

In this case, we need to get rid of any perfect cubes in the radicand.

Rewrite as `root(3)(64a^(12)b^(6)2a)` Then use `root(n)(ab)=root(n)(a)root(n)(b)` to get:

`root(3)(64a^(12)b^6)root(3)(2a)`

`=4a^4b^2root(3)(2a)` which is the simplified form.

** `root(3)(64)=4` since `4^3=64` . Also `root(3)(a^(12))=a^4` since `(a^4)^3=a^12` .

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes