How this calculator works
A positive integer exponent counts repeated multiplication. A negative exponent takes the reciprocal of the corresponding positive power. Positive bases also allow decimal exponents. Negative bases are accepted only with integer exponents in this real-number calculator. Results outside the numeric range produce an error.
Formula
Power = base^n. For base ≠ 0, base^(-n) = 1/base^n and base^0 = 1. For base > 0, base^n = exp(n × ln(base)).
Worked example
2^10 = 1024. A negative exponent gives 5^(-2) = 1/25 = 0.04. The decimal power 9^0.5 equals 3.
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Frequently asked questions
Why is 0^0 rejected?
Its meaning depends on the mathematical context. This calculator treats it as undefined rather than choosing a convention.
Why reject decimal powers of negative bases?
Some exact rational exponents have real results for negative bases, but a general decimal exponent does not identify that rational structure reliably. Only integer exponents are supported for negative bases.
Can I raise zero to a positive power?
Yes. Zero to any positive integer exponent is zero. Zero is rejected for a zero or negative exponent.