How to use this calculator
- Enter or choose base (b).
- Enter or choose exponent (n).
- The bⁿ updates as you type. Use Copy result or Share to keep it.
Method
bⁿ = b × b × … × b (n times); b⁻ⁿ = 1 ÷ bⁿ; b^(1/k) = the kth root of b; b⁰ = 1
- b
- the base
- n
- the exponent (power or index)
Worked example
- 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
- Doubling ten times: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
2 to the power of 10 is 1,024.
What the result means
A negative exponent means a reciprocal (2⁻³ = 1/8), and a fractional exponent means a root (9^0.5 = √9 = 3).
Assumptions and limits
- Answers are real numbers only.
- A negative base with a non-whole exponent, such as (−8)^0.5, has no real answer and is rejected. Cube roots of negatives need the exponent exactly 1/3, which a decimal cannot represent.
- Non-integer results are shown to 12 significant digits.
Questions
Why is any number to the power 0 equal to 1?
Each step down in power divides by the base: 2³ = 8, 2² = 4, 2¹ = 2, so 2⁰ = 2 ÷ 2 = 1. The same holds for every non-zero base.
What is 0 to the power 0?
It is taken as 1 by convention in algebra and combinatorics, which is what this calculator shows; in calculus it is treated as an indeterminate form.