Exponent Calculator
Raise any base to any exponent — including negative and fractional powers — and see the result in full, in scientific notation and as a reciprocal.
bⁿ multiplies b by itself n times.
How the exponent calculator works
bⁿ multiplies b by itself n times. A negative exponent is a reciprocal (2⁻³ = 1/8), a fractional exponent is a root (8^(1/3) = 2), and any non-zero base to the power 0 is 1. Very large or small results are shown in scientific notation.
Formula: bⁿ; b⁻ⁿ = 1 / bⁿ; b^(1/n) = ⁿ√b
Worked examples
| Inputs | Result | Note |
|---|---|---|
| 2¹⁰ | 1,024 | 1,024 |
| 10⁻³ | 0.001 | 0.001 |
| 8^(1/3) | 1.9999999999 | cube root ≈ 2 |
| 1.05²⁰ | 2.6532977051 | 20 years of 5% growth ≈ 2.65 |
FAQFrequently asked questions
What is a negative exponent?
A reciprocal: 2⁻³ = 1 ÷ 2³ = 0.125.
What is a fractional exponent?
A root: x^(1/2) is the square root, x^(1/3) the cube root, x^(3/2) the square root cubed.
What is anything to the power zero?
1, for any non-zero base. 0⁰ is left undefined.
Can a negative base have a fractional exponent?
Not in real numbers — (−8)^(1/3) is −2 by convention but (−8)^0.5 is imaginary. The calculator reports undefined.
How big can the result be?
Up to about 1.8 × 10³⁰⁸; beyond that it overflows to infinity.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.