Exponent Calculator
Calculator
How this was worked out
2 ^ 10 = 1,024
About this calculator
Raising a number to a power is repeated multiplication: the base is the number you start with and the exponent says how many times to multiply it by itself. This calculator evaluates base^exponent for any real base and any real exponent — whole numbers, negatives and fractions alike — so it doubles as a square-and-cube tool, a roots tool and a reciprocal tool. Type the two numbers and the result appears instantly, with scientific notation offered whenever the answer is very large or very small.
How to read your results
The big figure is the value of base^exponent. Below it you can read the same number in scientific notation (for example 1e+12 means 1 followed by twelve zeros), which is easier to scan once a result runs past a billion or drops below a ten-thousandth. If you raise a negative base to a fraction — say (−2)^0.5 — the calculator shows "No real result" instead of a number, because that power has no value among the real numbers; switch to a whole-number exponent or a positive base to get an answer.
How it's calculated
For a positive whole-number exponent n, base^n multiplies the base by itself n times, and base^0 = 1 for any base. A negative exponent is the reciprocal of the positive power: base^(−n) = 1 ÷ base^n. A fractional exponent is a root: base^(1/n) is the n-th root of the base, and base^(p/q) is the q-th root of base raised to the p-th power. A negative base only stays real when the exponent is a whole number or a fraction whose reduced denominator is odd (so (−8)^(1/3) = −2 is fine, but (−2)^0.5 is not). All input is validated as a finite real number before the power is evaluated.
Worked example
Base 2, exponent 10.
2^10 = 1024, because 2 is multiplied by itself ten times. Flip the exponent to −2 and you get 2^−2 = 1 ÷ 2² = 0.25 (the reciprocal of the square). Use a fractional exponent and 27^(1/3) = 3, the cube root of 27.
Frequently asked questions
What does a negative exponent mean?
A negative exponent is the reciprocal of the positive power. b^(−n) equals 1 ÷ b^n, so 5^−2 = 1 ÷ 5² = 1 ÷ 25 = 0.04. The base never becomes negative just because the exponent is negative — it simply moves to the denominator.
How does a fractional exponent work?
A fractional exponent is a root. b^(1/n) is the n-th root of b, so 27^(1/3) = 3 (the cube root of 27) and 2^0.5 = √2 ≈ 1.4142. More generally b^(p/q) is the q-th root of b, raised to the power p.
Why does (−2)^0.5 say "No real result"?
Taking an even root of a negative number has no real answer — there is no real number that squares to −2. Such powers exist only in the complex numbers. A negative base raised to a fraction is real only when the reduced denominator is odd, like (−8)^(1/3) = −2.
Is 0^0 equal to 1?
This calculator returns 0^0 = 1, following the common combinatorial convention also used by most programming languages and spreadsheets. The expression is sometimes called indeterminate in the context of limits, but as a discrete power it is taken to be 1 here.
Sources
- Power — Wolfram MathWorld
- Exponentiation — Wikipedia
Reviewed by the YouCalc Team · Last reviewed
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