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Why is there an inconsistency for (-1)^0.6 (or (-1)^(6/10)). I know in school I was taught to simplify the exponent to 3/5, which results in -1. However, when I leave the exponent as 6/10, I get a either the 10th root of (-1)^6 = 1 or ((-1)^(1/10))^6. Is there a way this can be explained without just simply saying to simplify the rational exponent first?

E.Eckstein
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    At the simplest, $(x^a)^b$ does not generally equal $x^{ab}$ when $x$ is not positive. (The simplest example of why it won't work is to compare $(-1)^{2*(1/2)}$ with $((-1)^2)^{1/2}$). There are a bunch of more detailed answers explaining this already on the site. Hopefully someone will drop a link to them here, or you can search for them. – JonathanZ Oct 12 '20 at 19:16
  • Thanks Hans. I'll have a look. – E.Eckstein Oct 12 '20 at 19:28

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