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Zero Exponents

Many beginning students think it's weird that anything raised to the power of 0 is 1. (I hear a lot of people say "It should be 0!") You can use the product of powers property to show why this must be true.

7⁰ × 7¹ = 7^{(0 + 1)} = 7¹

We know 7¹ = 7. So, this says that 7⁰ × 7 = 7. What number times 7 equals 7? If we try 0, we have 0 × 7 = 7. No good. The only number that works is 1.

In general, for all real numbers a, a ≠ 0, we have:

a⁰ = 1

Note that 0⁰ is undefined. (Click here to see why.)