Exponent Calculator
Any number raised to any power, with whole-number results shown exactly in full, and the cases a plain calculator gets wrong handled properly.
Result
Result: 1,024
Whole-number results beyond 15 digits are also shown exactly in full.
- In scientific notation
- 1.024 × 10^3
- Base to the negative exponent
- 0.000977
https://calcgallery.com/algebra-numbers/exponent-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Exponent Calculator
- Enter the base, the number being multiplied by itself.
- Enter the exponent, which can be negative or a fraction.
- Read the result, and for large whole-number powers, the exact value in full.
The rules
aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿa⁰ = 1 a⁻ⁿ = 1 ÷ aⁿ a^(1/n) = the nth root of aA fractional exponent p/q means the qth root of a raised to the power p. That is why an exponent of 1/3 on a negative number gives a real cube root, and 1/2 does not.
Very large and very small results
Results beyond about 10³⁰⁸ are too large for the numbers a computer uses, and the page says so instead of showing infinity. Results are also given in scientific notation, which is easier to read at any size.
With your numbers
- 2^10 = 1,024
Quick reference
Whole-number results beyond 15 digits are also shown exactly in full.
| Example | Result |
|---|---|
| 2 to the 10 | 1,024 |
| 2 to the −3 | 0.125 |
| 0 to the 0 | 1 |
| −8 to the 1/3 | -2 |
| −4 to the 0.5 | |
| 2 to the 60 | |
| 10 to the 400 |
Common questions about the Exponent Calculator
- What is 0 to the power 0?
- The page gives 1. That is the convention in algebra, combinatorics and computer arithmetic, because it keeps formulas such as the binomial theorem and power series working without exceptions. As a limit, 0⁰ has no single value: x⁰ tends to 1 but 0^x tends to 0, which is why it is sometimes called indeterminate.
- What does a negative exponent mean?
- One over the positive power: 2⁻³ = 1 ÷ 2³ = 1/8 = 0.125. Each step down in the exponent divides by the base once more.
- Why do some calculators say −8 to the 1/3 is an error?
- Because they compute powers through logarithms, which only work for positive numbers. But the cube root of −8 is simply −2, since (−2)³ = −8. This page recognises exponents that are fractions with an odd denominator and gives the real result. With an even denominator, such as −4 to the 1/2, there is no real answer: the result is the complex number 2i.
- Why show the exact value separately?
- Ordinary computer numbers hold about 15 to 17 significant digits. 2⁶⁰ is 1,152,921,504,606,846,976, nineteen digits; for whole-number powers the page also computes the exact integer, digit for digit, and shows it in full.