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Hi Deepankar,
This is very interesting to hear.
But please note that, the statement you have mentioned is applicable to only powers of positive integers.
For Example x-2 = 4, still has two roots (It does not make sense to say it has -2 number of roots).
Coming to your case.
x0 = 0, infact has no roots, in real numbers (it cannot have infinite roots).
Infact it is x0 = 1 is what will have infinite roots.
Imagine it like this:
Consider the log 1 to the base of some positive number "x" ( not equal to 1).
As log(1) is always 0, to any positive base, this will have infinite solutions.
Hence x^0 = 1 has infinite solutions.
Best Regards,
Ashwin (IIT Madras).
X^0=0 has no roots however x^0=1 has infinite roots. Infact every real no. excluding 0 is one of the equations.
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