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Name: Unknown
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Date: Around 1995

Why does 10 to the 0 power equal 1 and not 0?

Where does the idea of "zero power" come from? Well, for positive integer M and any number x, we define x^M = x * x * . . . * x where there are M factors of x on the right-hand side. By considering specific cases we may convince ourselves of the rule (x^M)/(x^N) = x^(M-N) for non-zero x and integers M and N with M > N (we just cancel N common factors of x from the numerator and denominator); and by asserting that this rule continues to hold even if M < N or M = N, we define x^K for K = M - N being a negative integer or zero. In particular, when M = N (that is, when K=0) we have the result x^0 = (x^M)/(x^M) which equals 1 (provided x is not zero, because for x = 0 the division is not defined). Thus, 10^0 = 1. (In fact, there is no number P such that 10^P = 0.)


Here is an answer which might be more intuitive. Remember that

10^a x 10^b = 10^(a + b). Then 10^0 can be written as

10^0 = 10^(-1) x 10^1 = (1/10) x 10 = 1

This is an example of what was stated in the first message, but less verbose.


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