posted by Luci on .
I'm supposed to evaluate the following equation in the real number system f possible : (-9)^1/2.
The answer says it's not possible; why, I don't understand this.
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.
oh, okay, I see; thank you very much! :D