Why is a number to the power of 0 equal to 1?
This is a question that I have been asked a number of times. The answer is
that if you want the rules of exponents to be true then you are forced to adopt
the convention that a to the zero is one. (I am going to write a^b to mean a
to the power b.) One of the rules of exponents is that if a is not
zero then (a^b)/(a^c) = a^(b-c). If b = c then (a^b)/(a^c) = (a^b)/(a^b) = 1,
so if we want this rule to be true then 1 = a^(b-c) = a^(b-b) = a^0.
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