For the problem [imath]((-1)^2)^{1/2}[/imath] it seems there are two valid ways to go about it, but you get two different answers.
Method 1: First calculate [imath](-1)^2 = 1[/imath] and then take the square root of [imath]1^{1/2} = 1[/imath].
Method 2: First multiply the exponents as in [imath](-1)^{2*1/2} = (-1)^1 = -1[/imath].
Method 3: Switch the exponents [imath]((-1)^{1/2})^2[/imath] and try to first take the square root of -1, but this is invalid.
The first two both seem valid to me in that they use valid exponent rules, but give different answers. So what am I missing and how would you handle this kind of situation?
Method 1: First calculate [imath](-1)^2 = 1[/imath] and then take the square root of [imath]1^{1/2} = 1[/imath].
Method 2: First multiply the exponents as in [imath](-1)^{2*1/2} = (-1)^1 = -1[/imath].
Method 3: Switch the exponents [imath]((-1)^{1/2})^2[/imath] and try to first take the square root of -1, but this is invalid.
The first two both seem valid to me in that they use valid exponent rules, but give different answers. So what am I missing and how would you handle this kind of situation?
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