Q:

# Why does a number to the zero power equal one?

A:

The concept of a number raised to the zero power equals one can be explained in several ways and is based on basic multiplicative concepts. Looking at the pattern established when a number is raised to different powers, each one less than the next, helps explain the concept.

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When a number such as 2 is raised to different powers, a particular pattern is seen as the exponent changes:

2^6 = 2*2*2*2*2*2 = 64
2^5 = 2*2*2*2*2 = 32
2^4 = 2*2*2*2 = 16
2^3 = 2*2*2 = 8
2^2 = 2*2 = 4
2^1 = 2

As the exponent value moves from 6 to 1, we see that the resulting values are reduced, consecutively, dividing by 2: 64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4 and 4/2 = 2. Extrapolating from this pattern, an exponent of 0 will result in an answer of 2/2 = 1, proving 2^0 = 1.

The number 2 was used to provide an example; however, this concept applies to all nonzero numbers.

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