Name: Unknown
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:

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



Replies:

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.)




rcwinther






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.




Unknown








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