Negative Exponent
A negative exponent means reciprocal.
Formula
Live Calculator
MembersVariables
Example
2⁻³ = 1/8
How it works
A negative exponent tells you to take the reciprocal of the base raised to the positive exponent. That works because division by a number is the same as multiplying by its inverse, so each step down in exponent corresponds to moving one factor from the numerator to the denominator. In other words, powers continue the pattern of repeated multiplication even when the exponent is negative.
When to use it
Use this when simplifying expressions with powers, especially in algebra and scientific notation. It is also useful when moving factors between the numerator and denominator in fractions.
Worked example, step by step
Evaluate 5⁻² 5⁻² = 1 / 5² 5² = 5 × 5 = 25 So, 5⁻² = 1/25
Common mistakes to avoid
- making the base negative instead of the exponent negative
- writing a^{-n} as -a^n instead of 1/a^n
- forgetting to keep the base the same when taking the reciprocal
Did You Know?
A negative exponent means "reciprocal", so 10⁻³ is one-thousandth — the basis of scientific notation for tiny numbers.
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.