Exponent Calculator
Enter a base and an exponent to get a^b as a decimal and in scientific notation. Negative and fractional exponents are supported.
Last updated November 4, 2026
Any real number.
Negative and decimal exponents work. Type 0.5 for a square root.
Result
2^10 = 1,024
| Form | Value |
|---|---|
| Decimal | 1024 |
| Scientific notation | 1.024 × 10^3 |
Show the work
Formula: a^b: multiply a by itself b times; a^(-b) = 1 / a^b; a^(1/n) is the n-th root of a.
- You entered base 2 and exponent 10.
- Multiply 2 by itself 10 time(s) (any number to the power 0 is 1).
- 2^10 = 1,024.
- Scientific notation: 1.024 × 10^3.
Result: 2^10 = 1,024
How exponents work
a^b = a × a × ... × a (b times)
a^(-b) = 1 / a^b
a^(1/n) = n-th root of a
a^0 = 1
A positive whole exponent counts how many times the base is multiplied by itself, so 2^10 = 1,024. A negative exponent flips the result into a reciprocal: 2^-3 = 1 / 2^3 = 1/8 = 0.125.
A fractional exponent is a root: 9^0.5 is the square root of 9, which is 3, and 8^(1/3) is the cube root of 8, which is 2. Type 1/3 as a decimal, which gives a result accurate to about 12 digits.
Results use standard double-precision arithmetic, so very long decimals are rounded to about 12 significant digits.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Undefined cases and limits
0 to the power 0 is treated as undefined, and 0 to a negative power would divide by zero. A negative base with a non-integer exponent, such as (-8)^0.5, has no real result, so it is rejected.
Results above 1e308 or too close to zero to store are reported as out of range rather than shown wrongly. Huge but valid answers are shown in scientific notation only.
How to use the Exponent Calculator
- Enter the base a, which can be negative or a decimal.
- Enter the exponent b, which can be negative or a decimal.
- Read the decimal result and the scientific notation. A negative exponent also shows the reciprocal form.
- Open Show the work to see how the result is built, or Copy, Print or Share it.
Worked example
2 to the power 10 is 1,024, or 1.024 × 10^3. With the exponent -3, 2^-3 = 1/8 = 0.125.
| Expression | Decimal | Scientific |
|---|---|---|
| 2^10 | 1024 | 1.024 × 10^3 |
| 2^-3 | 0.125 | 1.25 × 10^-1 |
| 9^0.5 | 3 | 3 × 10^0 |
| (-2)^3 | -8 | -8 × 10^0 |
| 2^100 | too large to print in full | 1.2676506002 × 10^30 |
Frequently asked questions
What does a negative exponent mean?
It means a reciprocal. a to the power -b equals 1 divided by a to the power b, so 10^-2 is 1/100 or 0.01.
Why is 0 to the power 0 undefined here?
Different rules give different values for it, so the calculator refuses to pick one and shows an error message instead.
Can I raise a negative number to a decimal power?
Not with real numbers. A negative base needs a whole-number exponent, because (-8)^0.5 would be a square root of a negative number. For the same reason (-8)^(1/3) is rejected by design, even though the real cube root of -8 is -2.
How large an answer can it show?
Anything up to about 1e308. Larger results are rejected as too large instead of being shown as infinity.