Raise any number to a power. This free exponent calculator handles positive, negative and fractional exponents — squares, cubes, reciprocals and roots — with scientific notation.
Enter a base and an exponent to compute the power. Exponents can be negative (reciprocal), fractional (roots) or decimal — for example 2⁻¹ = 0.5 and 27^(1/3) = 3.
An exponent (or power) tells you how many times to multiply the base by itself. A negative exponent means the reciprocal; a fractional exponent means a root.
How the Exponent Calculator Works
An exponent tells you how many times a base number is multiplied by itself. This calculator raises any base to any power — whole, negative, or fractional — and also reports the reciprocal, the square, and scientific notation for the result.
Formula: Result = base ^ exponent. A positive whole exponent multiplies the base by itself that many times (2^3 = 2 × 2 × 2 = 8). A negative exponent takes the reciprocal (2^-1 = 1 ÷ 2 = 0.5). A fractional exponent takes a root (9^0.5 = √9 = 3). A negative base combined with a fractional exponent has no real result and is not calculated, and a zero base with a negative exponent is undefined.
- Base — the number being raised to a power (the “b” in b^e)
- Exponent (power) — how many times the base is multiplied by itself; negative values invert the result, fractional values take a root
Example Scenarios
| Base | Exponent | Result |
|---|---|---|
| 2 | 10 | 1,024 |
| 5 | 3 | 125 |
| 2 | -1 | 0.5 |
| 9 | 0.5 | 3 |
| 10 | -2 | 0.01 |
| 3 | 4 | 81 |
Exponent Calculator FAQ
What does a negative exponent mean?
A negative exponent means “take the reciprocal.” For example, 2^-3 equals 1 divided by 2^3, or 1/8 = 0.125. The base doesn’t change sign — only the position of the result relative to 1 flips, since any negative exponent produces a value between 0 and 1 for a base greater than 1.How do I calculate a fractional exponent like 27^(1/3)?
Enter 27 as the base and 0.333333 (or as close to 1/3 as you can type) as the exponent. A fractional exponent represents a root, so 27^(1/3) asks “what number cubed gives 27?” — the answer is 3. Enter the decimal form of the fraction since the exponent field only accepts numbers.Why does the calculator reject a negative base with a fractional exponent?
Fractional exponents represent roots, and even roots of negative numbers (like the square root of -9) aren’t real numbers. Since the calculator can’t tell whether your fraction implies an even or odd root, it declines to guess and shows no result for negative bases raised to fractional powers.What happens when the base is 0 and the exponent is negative?
A negative exponent means taking the reciprocal of the base raised to a positive power, which would require dividing by zero. Because that’s undefined, the calculator won’t return a result when the base is 0 and the exponent is negative.How is the reciprocal value different from the square of the result?
The reciprocal is 1 divided by your answer (1 ÷ result), which flips the value — useful for checking negative-exponent relationships. The square of the result multiplies the answer by itself (result × result), showing what you’d get if you doubled the original exponent.How do I read the scientific notation output?
The scientific notation field shows your result as a number between 1 and 10 multiplied by a power of 10, formatted like “1.0240×10^3” for 1024. It’s most useful when the base and exponent produce a very large or very small result that’s hard to read in standard decimal form.Related Calculators
If you’re working with powers and roots, the square root calculator handles the inverse operation for fractional exponents like 0.5, while the scientific notation converter is handy for reformatting very large or very small exponent results. For a broader range of operations on the same numbers, try the scientific calculator.