Why is 10 to the power 0 equal to 1?

Reason 1

103 = 1 x 10 x 10 x 10

102 = 1 x 10 x 10

101 = 1 x 10

100 = 1

Reason 2102 ÷ 102 = 102 - 2 = 100 = 1 Reason 3code for calculating 10^n:

input n

x = 1

for i=1 to n

x = 10 * x

next i

print x

Reason 4Look at this:

103 = 10 x 10 x 10

102 = 10 x 10

101 = 10

So far so good. Now let's look at the negative exponents:

10-3 = 1 / (10x10x10)

10-2 = 1 / (10 x 10)

10-1 = 1 / 10

What should go in between -1 and 1? 0, but what value should we be giving to 0 anyway? Sounds tricky... or is it? Recall that exponents are based on multiplication. So maybe we can multiply 1/10 by 10 to find out what the value should be.

Going back, we can see the following:

101 = 10

100 = ?

10-1 = 1 / 10

So:

(1 / 10) * 10 = 1

Reason 5:given: 10x/10x=1

10x/10y=10x-y

now, 10 to the power 0 = 10x-x

=10x/10x

=1

since the powers can "cancel" each other

Reason 6:

given two nonnegative integers a and b, if A is a set with a elements and B is a set with b elements, then there are b^a mappings whose domain is A and codomain is B. If A is an empty set (a=0), the only one mapping is the empty one.

Reason 7:

if s is a positive real number, by definition, s^p = exp(p*ln(s)), exp is the exponential function and ln the natural logarithm. If p=0, s^p = exp(p*ln(s)) = exp(0) = 1.