Why is it that any base to the power of zero is 1?

Answer 1

To explain, let's examine the following statements

103, 102, 101, 100, 10-1, 10-2, 10-3

103= 1*10*10*10

102= 1*10*10

101= 1*10

100= 1

10-1= 1/10

10-2= 1/(10*10)

10-3= 1/(10*10*10)

103 ÷ 10-3 = 103 - 3 = 100 = 1

10-1*101 = 1

(1 / 10) * 10 = 1

Let r be a positive real number,

ln the natural logarithm and

exp the exponential function, defined

r^p = exp(p*ln(r))

p=0

r^p = exp(p*ln(r)) = exp(0) = 1.