Exponent Calculator
Raise any base to any power — including negative and fractional exponents
Related calculators
All utility & math- Quadratic Equation SolverSolve ax²+bx+c=0 — roots, discriminant, and vertex
- Slope CalculatorSlope, line equation, distance, and midpoint from two points
- Logarithm Calculatorlog base b, natural log (ln), log₁₀, and log₂
- Square Root CalculatorSquare root, cube root, or nth root with simplified radical
- LCM & GCD CalculatorLeast common multiple and greatest common divisor (GCF/HCF)
- Prime Factorization CalculatorPrime factors, primality check, and all divisors of a number
Quick summary
Enter a base and an exponent to compute the power. 2^10 = 1,024. A negative exponent gives the reciprocal (2^−3 = 1/8 = 0.125), and a fractional exponent is a root (9^0.5 = √9 = 3). Large or small results are also shown in scientific notation. Note a negative base with a fractional exponent has no real result.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
What is an exponent?
An exponent (or power) tells you how many times to multiply a base by itself. In 2^5, the base 2 is multiplied five times: 2×2×2×2×2 = 32. The exponent is written as a superscript. This calculator handles whole, negative, and fractional exponents.
What does a negative exponent mean?
A negative exponent means the reciprocal of the positive power: a^−n = 1 / a^n. So 2^−3 = 1/2^3 = 1/8 = 0.125. It doesn't make the result negative — it flips it into a fraction. The calculator shows the reciprocal alongside the result.
What is a fractional exponent?
A fractional exponent is a root: a^(1/n) is the nth root of a, and a^(m/n) is the nth root of a raised to m. For example, 9^(1/2) = √9 = 3 and 8^(2/3) = (∛8)² = 4. This lets one operation express both powers and roots.
Why can't I raise a negative number to a fractional power?
Because it would require an even root of a negative number, which has no real value (for example (−4)^(1/2) = √−4 is imaginary). The calculator flags this rather than returning an error, since the answer lies in complex numbers.
Key terms
- Base
- The number being multiplied by itself.
- Exponent
- How many times to multiply the base (the power).
- Reciprocal
- 1 divided by the value; what a negative exponent produces.
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.