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

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embizze | High School Teacher | (Level 2) Educator Emeritus

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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:


`=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` .

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