A whole-number power
2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Exponent calculator
Result
Fill in the fields to see your result.
How it works
For a whole-number exponent, the result is literally the base multiplied by itself that many times, which this shows explicitly. A negative exponent means the reciprocal of that product; a fractional exponent is a root.
Solving for the base uses a root (the inverse of raising to a power); solving for the exponent uses a logarithm (the inverse of exponentiation) — the same relationship read three different ways.
Formulas used
Result
result = aⁿ
Base
a = result^(1/n)
Exponent
n = log(result) ÷ log(a)
Worked examples
Solving for the exponent
If 2ⁿ = 32, then n = 5, since log(32) ÷ log(2) = 5.
Assumptions and limits
- All calculations use real numbers — some inputs (like a negative base with a fractional exponent) have no real-number answer.
Frequently asked questions
What does a negative exponent mean?
a⁻ⁿ equals 1 ÷ aⁿ — the reciprocal of the positive-exponent result. For example, 2⁻³ = 1 ÷ 8 = 0.125.
What does a fractional exponent mean?
a^(1/n) is the nth root of a — for example, 8^(1/3) is the cube root of 8, which is 2.
Why is there no real base for some inputs?
If the exponent is even, no real number raised to it can produce a negative result — squaring, for instance, always gives a non-negative number.
What is a to the power of zero?
Any nonzero number to the power of zero equals 1 — this keeps the pattern of exponent rules consistent (aⁿ ÷ aⁿ = a⁰ = 1).
Updated
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