Zero Exponent
Any nonzero number to the power zero is one.
Formula
Variables
Example
99^0 = 1
How it works
The zero exponent rule says that any nonzero base raised to the power 0 equals 1. This fits the pattern of dividing by the same number repeatedly: for example, 5^3 = 125, 5^2 = 25, 5^1 = 5, and 5^0 must be 1 so the pattern keeps working as each step divides by 5. The rule does not apply to 0^0, because zero cannot be used as the base here.
When to use it
Use this rule when simplifying expressions with exponents, especially in algebra and scientific notation. It also helps when reducing formulas or checking patterns in powers of the same number.
Worked example, step by step
Evaluate 7^0 Step 1: Identify the base: a = 7 Step 2: Apply the zero exponent rule: a^0 = 1 for any nonzero a Step 3: So, 7^0 = 1 Final answer: 1
Common mistakes to avoid
- Thinking that 0 means the answer should be 0
- Using the rule on 0^0, which is not allowed here
- Confusing the zero exponent rule with the power of one rule, a^1 = a
Did You Know?
Any non-zero number to the power zero equals 1, a convention that keeps the laws of exponents consistent.
Share this formula
More in Algebra
View allQuadratic Formula
IntermediateFinds the roots of any quadratic equation ax² + bx + c = 0.
Discriminant
IntermediateDetermines the nature of the roots of a quadratic equation.
Binomial Theorem
IntermediateExpands any power of a binomial into a sum of terms.
Logarithm Product Rule
IntermediateThe logarithm of a product equals the sum of logarithms.
Logarithm Quotient Rule
IntermediateThe logarithm of a quotient equals the difference of logarithms.
Logarithm Power Rule
IntermediateThe logarithm of a power equals the exponent times the logarithm.