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It is a consequence of the isomorphism between powers of numbers under multiplication and their indices under addition.

This leads to the definition of x-a as the [multiplicative] inverse of xa.

Then xa * x-a = xa-a = x0

But since x-a is the inverse of xa, their product is 1.

That is to say, x0 = 1.

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Q: Why does any number with 0 power equals 1?
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