Powers: How to Calculate Base to the Exponent

Calculates base^exponent.

Explanation

A power is repeated multiplication: the base multiplied by itself as many times as the exponent says.

a^n = a \times a \times \cdots \times a

$a$ — the base, the number being multiplied
$n$ — the exponent, how many times the base is used as a factor
$a^n$ — the resulting value

Example

Take a base of 2 and an exponent of 10. Multiplying 2 by itself ten times gives

2^{10} = 1024

The powers of 2 double at every step: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. That last value is worth recognising, since 1024 bytes is what computing calls a kilobyte.

Notes

Any non-zero base raised to the power 0 is defined as 1. It is what keeps the rule $a^m \div a^n = a^{m-n}$ working when $m = n$ .
A negative exponent means a reciprocal: $2^{-3} = \dfrac{1}{2^3} = 0.125$ .
A fractional exponent means a root: $9^{0.5} = \sqrt{9} = 3$ .
A negative base with a fractional exponent often has no real value at all. $(-4)^{0.5}$ is not a real number.
The index laws hold throughout: $a^m \times a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$ . Large exponents make values grow explosively, so keep an eye on the number of digits.