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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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