Calculate any base raised to any power — including negative exponents, fractional exponents, and zero exponents. See a full powers table for any base.
| Property | Example | Rule |
|---|---|---|
| Zero exponent | b⁰ = 1 | Any base to the power 0 equals 1 |
| Negative exponent | b⁻ⁿ = 1/bⁿ | Reciprocal of positive exponent |
| Fractional exponent | b^(1/n) = ⁿ√b | nth root of the base |
| Product rule | bᵐ · bⁿ = bᵐ⁺ⁿ | Add exponents when multiplying |
| Power rule | (bᵐ)ⁿ = bᵐⁿ | Multiply exponents when raising a power |
| Expression | Value | Scientific |
|---|---|---|
| 2-3 | 0.125 | 1.250e-1 |
| 2-2 | 0.25 | 2.500e-1 |
| 2-1 | 0.5 | 5.000e-1 |
| 20 | 1 | 1.000e+0 |
| 21 | 2 | 2.000e+0 |
| 22 | 4 | 4.000e+0 |
| 23 | 8 | 8.000e+0 |
| 24 | 16 | 1.600e+1 |
| 25 | 32 | 3.200e+1 |
| 26 | 64 | 6.400e+1 |
| 27 | 128 | 1.280e+2 |
| 28 | 256 | 2.560e+2 |
| 29 | 512 | 5.120e+2 |
| 210 | 1024 | 1.024e+3 |
2^10 and 10^2 look like mirror images, yet one is 1,024 and the other is 100. People also expect a negative exponent to give a negative answer, when 2^-3 is a small positive 0.125, and read 8^(1/3) as division, when it is the cube root and equals 2. This calculator takes a base and an exponent, computes the power directly, and prints the same base raised to every exponent from -3 to 10 so you can see the pattern, not just one number.
For a positive whole exponent, b^n means b multiplied by itself n times. The page does not loop; it hands the base and exponent to JavaScript's Math.pow, which also handles the cases repeated multiplication cannot.
Those cases follow identities listed in the page's reference table: b^0 = 1, b^-n = 1 ÷ b^n, and b^(1/n) is the nth root of b. Exponents combine as b^m × b^n = b^(m+n) and (b^m)^n = b^(m×n). Two inputs break the pattern. Zero with a negative exponent shows 'cannot be raised to a negative exponent', and a negative base with a fractional exponent returns no real number in JavaScript, so the page prints undefined, even though the real cube root of -8 is -2.
Display rules: results above 10^15 or below 10^-7 switch to scientific notation with six decimals; anything else is rounded to 10 decimals. Under the result box, a scientific-notation line appears whenever the absolute value exceeds 999.
Example: $5,000 growing 7% a year for 30 years has a growth factor of 1.07^30. Enter base 1.07 and exponent 30 and the page returns 7.6122550427, with 7.612255e+0 as the scientific form. Then 5,000 × 7.6122550427 = 38,061.28, before contributions, fees and tax. With exponent -3, the same base gives 0.8162978769, the factor for discounting three years back.
If you enter -2 as the base and 2 as the exponent, the page treats -2 as the base and returns 4. For the textbook -2^2 = -4, where only the 2 is squared, enter 2 and 2 and negate the answer yourself.
Either the base is negative and the exponent is fractional, or the number is too large to store, which happens beyond roughly 1.8 × 10^308. In the powers table an overflowing row shows the infinity sign.
The page returns 1, the usual convention in algebra and combinatorics. In calculus 0^0 is treated as an indeterminate form, so check which convention your course uses.
About 15 to 16 significant digits. 2^60 is shown as 1.152922e+18, but the exact value is 1152921504606846976. For exact whole-number powers up to an exponent of 1000, use the Big Number calculator.
No. The box reads only the leading number, so 1/3 is read as 1 and you get the base back unchanged. Type 0.3333333333 instead, which gives 2.9999999997 for 27. That is close but not exactly 3, so for roots the Root calculator is the better tool.