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That x^0=1 is a convention which makes formulae nicer. There is no "proof" of it. For instance, sometimes it is more useful to set 0^0=0. The philosophy is that 1 is the neutral element for multiplication, so if we multiply nothing (i.e. ^0), we stay with the neutral element. Much as if we add nothing, we get 0, the neutral element for addition.
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Didn't remember how intense love could be... Thank you B.
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