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Question from Manny:

Hello,

Can you explain why this is wrong:
-1 = (-1)^3 = (-1)^{6/2} = ((-1)^6)^{1/2} = (1)^{1/2} = 1 ??

We can show the same with other numbers :
-2 = (-2)^{2/2} = 2...

Thank you

Hi Manny,

The problem is the very last step. $1^{1/2}$ is any number $x$ such that $x \times x = 1.$ Both $x=1$ and $x=-1$ satisfy $x \times x = 1.$ Thus $1^{1/2} = \pm 1.$

I hope this helps,
Penny

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