Powers in brief
bⁿ means multiplying b by itself n times: 2¹⁰ = 2 × 2 × … × 2 (ten times) = 1,024. Three rules cover most cases:
- Zero exponent: b⁰ = 1 for any b ≠ 0.
- Negative exponent: b⁻ⁿ = 1/bⁿ, so 10⁻³ = 1/1,000 = 0.001.
- Fractional exponent: b^(1/n) is the n-th root, so 9^0.5 = √9 = 3 and 8^(1/3) = 2. b^(m/n) = (n-th root of b)ᵐ.
Powers of 2 count memory and colours (2²⁴ = 16,777,216 colours in 24-bit images), powers of 10 express scale, and fractional powers appear in physics and finance formulas such as compound growth.
Worked example
1.07²⁰ is how much an amount grows in 20 years at 7% a year: about 3.8697, so money nearly quadruples.
How this works
The page computes base raised to exponent with standard double-precision arithmetic, which is exact for whole-number results such as 2¹⁰ and accurate to about 15 significant digits otherwise. Negative exponents give reciprocals and fractional exponents give roots. A negative base with a non-whole exponent, such as (−8)^0.5, has no real-number answer and is reported instead of showing NaN. The expression is also shown in superscript form. Everything runs in your browser.
Frequently asked
What is any number to the power 0?
1, for any number other than 0. 0⁰ is conventionally taken as 1.
What does a negative exponent mean?
The reciprocal: 2⁻³ = 1/2³ = 1/8.
What does an exponent of 0.5 mean?
The square root: 25^0.5 = 5.
Why is (−8)^(1/3) shown as complex?
With floating-point fractional exponents, negative bases have no real result here. The real cube root of −8 is −2; use the root calculator for odd roots.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/math/exponent-calculator/