How this calculator works
This calculator raises any base to any exponent, including negative and fractional exponents, and shows the full result rather than a rounded approximation whenever that is practical. Enter a base and an exponent and the result updates instantly.
Exponent rules extend naturally past positive whole numbers. A negative exponent flips the base into a reciprocal, and a fractional exponent is the same operation as taking a root. When a result would need far more digits than a screen can usefully show, either because it is enormous or vanishingly small, the calculator switches to fixed-precision scientific notation so the value stays readable and honest about its precision.
The formulas
Positive integer exponent: b^n = b × b × ... × b (n times)Negative exponent: b^-n = 1 ÷ b^nFractional exponent: b^(1/n) = the nth root of bZero exponent: b^0 = 1 for any nonzero bBy convention, this calculator treats 0^0 as 1 — the value used in combinatorics and power series — though some fields leave it undefined. A negative base raised to a fractional exponent (other than a whole-number root case handled by the dedicated root calculator) produces a complex number, which is outside what this calculator computes.
Worked example: 2^10 and beyond
- 2 raised to the 10th power multiplies 2 by itself 10 times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024.
- A negative exponent is a reciprocal: 2^-3 = 1 ÷ 2^3 = 1 ÷ 8 = 0.125.
- A fractional exponent is a root: 9^0.5 = √9 = 3, and by the same rule 8^(1/3) = ∛8 = 2.
- 0^0 is shown as 1 in this calculator, following the widely used convention rather than leaving the field blank.
Frequently asked questions
What does a negative exponent mean?
A negative exponent means take the reciprocal of the base raised to the positive version of that exponent: b^-n = 1 ÷ b^n. For example, 5^-2 = 1 ÷ 25 = 0.04.
What does a fractional exponent mean?
A fractional exponent represents a root. b^(1/n) is the nth root of b, so b^0.5 is a square root and b^(1/3) is a cube root. A fraction like b^(2/3) is the cube root of b, squared.
Why does this calculator say 0^0 = 1?
0^0 is treated differently across mathematics: some contexts leave it undefined, but the convention 0^0 = 1 is standard in combinatorics, power series, and most programming languages, so that is what this calculator returns, with a note explaining the choice.
Can a negative base have a fractional exponent?
Only in special cases, such as odd-denominator roots handled by a dedicated root calculator. In general, a negative base raised to a fractional exponent produces a complex number rather than a real one, so this calculator returns a message instead of a misleading result.
Why do some results show in scientific notation instead of a plain number?
Very large or very small results are shown as a mantissa and exponent (like 1.152921505e+18) instead of a long string of digits, since double-precision arithmetic only reliably holds about 15 to 17 significant digits either way.