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?