Thread: Evaluating exponentiation with negative base and rational exponent

How come



is equal to



I know that it can be shown using several exponent laws but I thought those were only valid for a rational exponent as long as the base is positive. I have been told that negative bases rased to rational exponents is undefined. Somebody please help me sort this conundrum out!

Originally Posted by MathCrusader

How come



is equal to

That really is the cube-root of a quantity squared.


NOTE that cannot be because that the square root of a negative.

Alright thanks. I suppose if the base is negative and the denominator of the exponent is even is what causes problems. Thx again