Exponent Calculator
The calculator raises whole and decimal numbers to any power, including negative exponents, with an exact result and a step-by-step solution.
The exponent calculator raises whole and decimal numbers, including negative ones, to any whole power from −1000 to 1000. The result is exact, with no rounding, even when it has thousands of digits.
What is a power of a number
A power an is the product of n equal factors a. The number a is called the base, and n is the exponent.
an = a · a · … · a (n times)
Example. 25 = 2 · 2 · 2 · 2 · 2 = 32
Rules worth knowing
| Rule | Example |
|---|---|
| a1 = a | 71 = 7 |
| a0 = 1 (a ≠ 0) | 150 = 1 |
| a−n = 1 / an | 2−3 = 1/8 = 0.125 |
| am · an = am+n | 32 · 33 = 35 = 243 |
| (am)n = am·n | (23)2 = 26 = 64 |
Powers of negative numbers
A negative number raised to an even power gives a positive result, and to an odd power a negative one:
(−2)4 = 16, (−2)3 = −8
Note that −24 and (−2)4 are different expressions. In the first one only 2 is raised to the power and the minus comes afterwards: −24 = −16. The calculator takes the base together with its sign, so it calculates (−2)4.
Negative exponents
A power with a negative exponent is one divided by the same power with a positive exponent. The calculator gives the answer as a fraction in lowest terms and as a decimal.
Example. 0.4−3 = (2/5)−3 = (5/2)3 = 125/8 = 15.625