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## Homework Statement

Show that if m and n are positive integers, [itex]m \ne 0[/itex], and if n/m is an irreducible fraction, then the set of values of [itex]z^{n/m}[/itex] defined by [tex](z^{1/m})^n[/itex] is identical to the set of value of [itex](z^n)^{1/m}[/itex]

I need to prove the case of a reducible fraction as well, where the two expressions aren't equal.

## The Attempt at a Solution

I've been staring at this for a day now and I don't see where to start this beyond messing with the expressions in polar form... hints? Thanks.

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Side question:

[itex](8^{2/3})(8^{-2/3})[/itex]

Does finding all three roots of each factor and then multiplying them in all combinations give all possible results of the above expression? Thanks.