Simplify the rational expression

Question

Simplify the Rational expression for when: n is even ⁿ√m³ⁿ and for when n is odd ⁿ√m³ⁿ

Answer 1

• We can think of both problems as (m³ⁿ)^1/n
• Using the exponent rule, we end up with m³
• This works fine if n is odd, as we can have a positive or negative value of an odd root. (n odd answer is m³)
• However, if n is even, we can only have a positive root, so we have to modify the answer with absolute value to |m³| (n even answer is |m³|)