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It is a consequence of the definition of the index laws.

xa * xb = xa+b

If you put b = 0 in the above equation, then you get

xa * x0 = xa+0

But a+0 = a so that the right hand side becomes xa

Thus the equation now reads

xa * x0 = xa

For that to be true for all x, x0 must be the identity element for multiplication. That is x0 = 1 for all x.

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