Exponent Calculator
Adjust the inputs below. Results update as you type.
How it works
b^n means multiply b by itself n times. Negative exponents: b^(−n) = 1/b^n. Fractional exponents: b^(1/2) = √b; b^(m/n) = ⁿ√(b^m). Zero exponent: any nonzero b^0 = 1. Scientific notation handles very large or small results. In compound interest, the exponent represents time periods—small rate differences compound dramatically over long periods.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
An exponent means repeated multiplication: aⁿ = a × a × … (n times). Rules include aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, and a⁻ⁿ = 1/aⁿ.
Worked example
2⁵ = 2×2×2×2×2 = 32. And 10³ × 10² = 10⁵ = 100,000.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What does a negative exponent mean?+
It is the reciprocal: a⁻ⁿ = 1/aⁿ. So 2⁻³ = 1/8 = 0.125.
What is anything to the power of zero?+
Any nonzero number raised to the power 0 equals 1, by the rules of exponent division.
What is a fractional exponent?+
It represents a root: a^(1/n) is the nth root of a. So 9^(1/2) = √9 = 3.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.