Zero exponent: key idea
When a nonzero number or expression is raised to the power 0, the value is 1. This is the rule to use when simplifying expressions with a zero exponent.
How to simplify
- Look for the exponent. If the exponent is 0, the base becomes 1.
- Keep an eye on the base. The base must be nonzero for this rule to apply.
- Replace the expression with 1. For example, any valid expression like (a^0) simplifies to (1).
- Finish the expression. If the zero-power term is part of a larger expression, simplify the rest normally.
Examples
- (7^0 = 1)
- ((3x)^0 = 1) as long as (3x \neq 0)
- (5y^0 = 5), because only (y^0) becomes 1
Check your work
Ask yourself: is the base nonzero, and did I replace the zero exponent with 1? If there are other factors, make sure they are simplified correctly too.
Common mistake
Do not write the base itself as the answer. The result of a zero exponent is 1, not the original number.