Exponent Calculator
Raise any number to any power, including negative and fractional exponents, to 30 significant digits.
About the Exponent Calculator
An exponent says how many times to multiply the base by itself: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A negative exponent means a reciprocal (2⁻³ = 1/8), and a fractional exponent means a root (8^(1/3) = ∛8 = 2).
The formula
aⁿ = a × a × … × a (n times)
- a⁻ⁿ
- 1 ÷ aⁿ
- a^(1/n)
- n-th root of a
- a⁰
- 1, for any a ≠ 0
Powers of 2
| n | 2ⁿ |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 4 | 16 |
| 8 | 256 |
| 10 | 1024 |
| 16 | 65536 |
| 20 | 1048576 |
| 32 | 4294967296 |
| 64 | 18446744073709551616 |
Worked example
Example: 3^5 = 243
- Inputs: Base: 3; Exponent: 5.
- Formula: aⁿ = a × a × … × a (n times)
- A power is repeated multiplication: 3^5 = 3 × 3 × 3 × 3 × 3
- Multiply: = (243)
- Result: 3^5 = 243
- Scientific notation: 2.43e+2
Questions people ask
What is anything to the power 0?
1 (except 0⁰, which is usually left undefined or taken as 1 by convention).
Why is (−8)^(1/3) allowed but (−8)^(1/2) not?
Odd roots of negatives are real (−2); even roots aren't.