Zero Exponent
Any nonzero number to the power zero equals one.
Formula
Variables
Example
7⁰ = 1, and (−3)⁰ = 1 — any nonzero base to the zero power is 1.
How it works
A zero exponent tells you there are no factors of the base left in the product. The rule a^0 = 1 is set so the pattern of powers stays consistent: for example, a^3 ÷ a^3 = a^(3−3) = a^0, but any nonzero number divided by itself is 1. This only works for nonzero bases, because 0^0 is not defined in the same way.
When to use it
Use this rule when simplifying expressions with exponents, especially after dividing powers with the same base. It also appears when checking patterns in algebra and when reducing formulas to simplest form.
Worked example, step by step
Simplify 12^0. 12^0 means there are zero factors of 12. Any nonzero number raised to the zero power equals 1. So, 12^0 = 1.
Common mistakes to avoid
- Thinking the answer is 0 because the exponent is 0
- Using the rule for the base 0, as in 0^0 = 1
- Forgetting that the base must be nonzero
Did You Know?
Any nonzero number to the power 0 equals 1 — it must, to keep the exponent rules consistent.
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