Exponent Calculator
Calculate any base raised to any power — including negative, fractional, and decimal exponents. Get the result, scientific notation, and explanation.
What is Exponent Calculator?
The exponent calculator evaluates bn for any real base and exponent — positive, negative, fractional, or decimal. It also shows the result in scientific notation for very large or very small numbers.
Formula
An exponent indicates repeated multiplication: bn = b × b × … × b (n factors).
- b0 = 1 for any nonzero b
- b−n = 1 / bn (negative exponent flips to reciprocal)
- b1/n = ⁿ√b (fractional exponent is a root)
- bm/n = ⁿ√(bm)
Worked example
210 = 1,024 (memorable computer-science number — 1 KB).
3−2 = 1/9 ≈ 0.1111.
160.5 = √16 = 4.
How to use this calculator
- Enter the base (the number being raised).
- Enter the exponent (the power).
- The decimal result, scientific-notation form, and a plain-English reading appear instantly.
Frequently asked questions
Why is anything to the zero power equal to 1?
Because of the rule bm ÷ bm = bm−m = b0. Any nonzero number divided by itself is 1, so b0 = 1. The expression 00 is debated — most contexts treat it as 1 by convention.
What does a negative exponent mean?
It means take the reciprocal: b−n = 1 / bn. So 2−3 = 1/8 = 0.125.
What about a fractional exponent?
Fractional exponents are roots: b1/2 = √b, b1/3 = ∛b, b2/3 = ∛(b²).
Why does my calculator show "Complex" for a negative base?
(−2)0.5 is the square root of a negative number — undefined in the real numbers. Negative bases work cleanly only with whole-number exponents in real math.