MATH · EXPONENT
Exponent Calculator
Raise any base to any power — positive, negative, or fractional — with domain error detection for undefined results.
1024
2^10
About This Calculator
Exponentiation raises a base to a power: x^n. This calculator handles positive and negative integers, fractional exponents (roots), and large exponents, with clear error messages when the result is undefined in the real numbers.
How It Works
Enter a base and an exponent. The calculator returns the result to 10 significant figures. Errors are raised for 0^(negative) (Infinity), negative base with non-integer exponent (complex result), and results that overflow to Infinity. 0^0 equals 1 by mathematical convention.
The Formula
x^n = base × base × … (n times)
- x
- base
- n
- exponent
Frequently Asked Questions
- What is a negative exponent?
- A negative exponent represents a reciprocal: x^(−n) = 1 / x^n. So 2^(−3) = 1/8 = 0.125.
- What does a fractional exponent mean?
- A fractional exponent represents a root: x^(1/2) = √x, x^(1/3) = ∛x. More generally, x^(m/n) = nth root of x^m.
- Why is 0^0 equal to 1?
- 0^0 is mathematically indeterminate in analysis, but by convention it equals 1 in combinatorics and most computing contexts (e.g. the empty product). This calculator follows the convention.