I'm supposed to evaluate the following equation in the real number system f possible : (-9)^1/2.

Question

The answer says it's not possible; why, I don't understand this.

Answer 1

The problem is really how to define fractional powers like x^(1/2).

You want it to define in such a way so that the usual rules for taking powers still hold. E.g.:

(x^a)^b = x^(ab)

This means that you want to define
x^(1/2) such that:

(x^(1/2))^2 = x

So, x^(1/2) should be the square root of x. But this is only defined for positive x. The square of a real number is always positive, so if x is negative, no real number can be its square root.

Answer 2

oh, okay, I see; thank you very much! :D