Why is any number raised to the power of zero 1?

Answer 1

Consider this a definition, but a very useful one. Defining it this way, several rules about powers continue being valid for this special case. For example, consider the following:

100 x 103 = 103

This is valid according to the rule for adding exponents, since 0 + 3 = 3. Now, how much should the expression 100 be? Obviously the answer is one.

Here is another way to look at it. Consider the sequence:

103 = 1000

102 = 100

101 = 10

100 = ?

So, what's the value of the question mark? Note that on the left, the exponent goes down one at a time. On the right, each term is ten times less than the one on the previous line. Thus, the logical value to fill out the question mark seems to be one.