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I was taught in school that

$x^{a/b} = \sqrt[b]{x^a}$

however, wolfram says this is not always true:

$\sqrt[3]{x^2} \ne x^{2/3}$
http://www.wolframalpha.com/input/?i=cbrt%28x%5E2%29+%3D%3D%3D+x%5E%282%2F3%29

but also says:

$\sqrt[3]{x} = x^{1/3}$
http://www.wolframalpha.com/input/?i=cbrt%28x%29+%3D%3D%3D+x%5E%281%2F3%29

Is he right? If so, can anyone explain why?

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    Tha$n$k you, that pretty much explained everything.2011-10-19

2 Answers 2