Why does ten to the power of zero not equal zero?

Answer 1

Anything raised to the 0th power (except 0) is equal to 1.

The reason:

Consider the following sequence of numbers:

104, 103, 102, 101

Another way to write this sequence of numbers is

10000, 1000, 100, 10

Notice that each number is one-tenth of the preceding number.

1000 is one-tenth of 10000

100 is one-tenth of 1000

10 is one-tenth of 100.

What should the next number in the sequence be?

Looking at the first way of writing the numbers, it should be 100.

Looking at the second way of writing it should be one-tenth of 10. One-tenth of 10 is 1.

Similarly 10-1 would be the next number in the sequence and it would have to equal one-tenth of 1 or 0.1.