Exponent Calculator
Raise a base to a positive, negative or fractional power where a supported real result exists.
Power result
Real arithmetic with floating-point presentation. 0^0 and zero to negative powers are rejected. Negative bases require integer exponents. Overflow and underflow show limits rather than misleading finite values.
Formula checked · NumberSwift · Review process
How this calculator works
An integer exponent describes repeated multiplication; a negative exponent takes the reciprocal of the corresponding positive power. For a positive base, a fractional exponent can describe a root or other real power. Negative bases with integer powers remain real, with sign determined by parity. A decimal exponent does not reliably encode an exact rational denominator, so negative-base fractional powers are not inferred. Scientific Calculator provides cbrt for an explicit negative cube root.
Formula
Result = base^exponent. For nonzero base, base^(−n) = 1/base^n. For positive base, base^(1/n) is its positive nth root.
Assumptions & limitations
Real arithmetic with floating-point presentation. 0^0 and zero to negative powers are rejected. Negative bases require integer exponents. Overflow and underflow show limits rather than misleading finite values.
Worked example
2^8 = 256; 2^(−3) = 0.125; 9^0.5 = 3. A negative base gives (−2)^3 = −8 and (−2)^4 = 16.
Our approach to calculations ↗Common questions
Can I compute roots with fractional exponents?
Yes for nonnegative bases where defined, such as 16^0.5 = 4. Use explicit root functions for supported negative roots.
Why is a negative base with a decimal exponent rejected?
A decimal approximation may not represent an exact rational exponent. The result could require complex arithmetic, which this tool does not support.
Why not show zero for extremely tiny nonzero results?
Underflow can silently erase a nonzero mathematical value. The tool identifies that precision limit instead.