Power calculator
Enter the base and the exponent: calculate the result of the exponentiation.
What raising to a power means
Raising to a power means multiplying a number by itself as many times as the exponent says: 2⁵ is 2×2×2×2×2, that is 32. It's the operation that shows up whenever something grows by a fixed percentage over and over: a sum earning 3% a year for ten years is multiplied by 1.03¹⁰, and a population doubling every period is multiplied by 2 raised to the number of periods.
Exponents that aren't whole numbers
A negative exponent doesn't give a negative result: it gives the reciprocal, one divided by the power. So 10⁻² is 1/100 = 0.01, which is why the metric prefixes are written that way (milli is 10⁻³, micro is 10⁻⁶).
A fractional exponent is a root: raising to 0.5 is the square root (9^0.5 = 3), raising to 1/3 is the cube root. And any number raised to zero is 1, zero itself included: 0⁰ = 1 is a convention, not a law of nature, but it's the one every calculator uses because it keeps the formulas consistent.
When the result isn't a number, and when it's huge
A negative base with a decimal exponent has a result among the real numbers only if the exponent, written as a reduced fraction, has an odd denominator: (−32)^0.2 is −2, because 0.2 is 1/5 and the fifth root of a negative number exists. (−8)^0.5, on the other hand, would mean the square root of a negative number, which doesn't exist: in that case a dash appears here with the reason written underneath, not a number and not the infinity sign either, which would mean something else.
Big numbers, on the other hand, don't turn into infinity here. With a whole-number exponent the result is exact up to 10,000 digits: 2 raised to 2,000 has 603 of them, and they all appear; when it's a never-ending fraction, like 3 raised to −2, which is 1/9, the fraction appears with the rounded value next to it. Beyond 10,000 digits the result is written with a power of ten, and if it isn't exact the page says how many significant digits it's rounded to; above 10 raised to one billion the page doesn't calculate and says so.
Nearby tools
For the inverse operation, «what exponent do I need to get this number», there is Logarithm. For expressions with brackets and several operations the page is Scientific calculator, and for the multiples and submultiples of the metric system SI prefixes.