Exponent Calculator guide
Exponent Calculator: Powers and Indices
Use our exponent calculator to raise any number to a power, including negative and fractional exponents, or to find the exponent.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
An exponent (also called a power or index) tells you how many times to multiply a number by itself. Our Exponent Calculator works out any power, with exact answers for big results.
How to use the calculator (Exponent Calculator)
- Choose aⁿ to work out a power, or exponent n to find the power.
- Enter the base and the exponent (or the result).
The rules of indices
| Rule | Example |
|---|---|
| aᵐ × aⁿ = aᵐ⁺ⁿ | 2³ × 2² = 2⁵ = 32 |
| aᵐ ÷ aⁿ = aᵐ⁻ⁿ | 2⁵ ÷ 2² = 2³ = 8 |
| (aᵐ)ⁿ = aᵐⁿ | (2³)² = 2⁶ = 64 |
| a⁰ = 1 | 5⁰ = 1 |
| a⁻ⁿ = 1 ÷ aⁿ | 2⁻³ = ⅛ |
| a^(1/n) = ⁿ√a | 8^(1/3) = 2 |
A worked example
With the calculator's default settings, 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024.
Finding the exponent
To solve aⁿ = y, use logarithms: n = log(y) ÷ log(a). For example, 2ⁿ = 1,024 gives n = 10.
Frequently asked questions
Can I raise a negative number to a power?
Yes, for whole-number powers: (−2)³ = −8. Fractional powers of negative numbers aren't real numbers.
What's 0⁰?
It's usually taken to be 1.
How do I work with very big powers?
The calculator shows exact values for whole numbers up to thousands of digits. For more, try our Big Number Calculator.
For roots, use our Root Calculator, and for logs, our Log Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Exponentmathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.