Power calculator
Enter a base and exponent to calculate aᵇ, including decimal and negative exponents when the result is a real number.
Power (aᵇ)
Raise a base to an exponent.
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Result
Enter the values, then select Calculate.
How to use the power calculator
A power combines a base and an exponent. This calculator evaluates finite real-number powers in your browser and shows the equation used. It does not parse algebraic expressions or return complex numbers.
Power calculation: raise a base to an exponent
Power mode evaluates aᵇ. A positive whole-number exponent means repeated multiplication: 3⁴ = 3 × 3 × 3 × 3 = 81. An exponent of zero gives 1 for every nonzero base. A negative exponent takes the reciprocal, so 4⁻² = 1 ÷ 4² = 0.0625.
Decimal exponents are allowed when they have a real meaning for the chosen base. For example, 9⁰·⁵ is the square root of 9 and equals 3. A negative base with a non-integer exponent is rejected because JavaScript may otherwise return a non-real or ambiguous value. The tool also rejects 0⁰ and zero with a negative exponent instead of silently choosing a convention.
Power examples
Enter 2 as the base and 10 as the exponent to get 1,024. For a negative exponent, 2⁻³ = 0.125 because it means 1 ÷ 2³. A decimal example is 9⁰·⁵ = 3.
A negative base works with an integer exponent: (−3)³ = −27. It is rejected with a non-integer exponent because that result may not be a real number.
Limits and result precision
- Both inputs must be finite numbers.
- 0⁰ and zero raised to a negative exponent are reported as domain errors.
- Negative bases require an integer exponent.
- Very large or small finite answers may use scientific notation.
- Results use browser floating-point arithmetic; use specialist software when arbitrary precision is required.
Frequently asked questions
What does a negative exponent mean?
It takes the reciprocal: a⁻ⁿ = 1 ÷ aⁿ, provided the base is not zero.
Why does 0⁰ show an error?
Different contexts use different conventions, so this real-number calculator treats 0⁰ as undefined.
Can the exponent be a decimal?
Yes, when the base and exponent produce a real result, such as 9⁰·⁵ = 3.
Why is a negative base with a decimal exponent rejected?
Many such powers are non-real or ambiguous in decimal form. This tool only returns supported real-number results.
How can I check a power result?
For small integer exponents, multiply the base by itself the stated number of times; for negative exponents, also take the reciprocal.