Exponentiation (power) is an arithmetic operation on numbers. It is repeated multiplication, just as multiplication is repeated addition. People write exponentiation with upper index. This looks like this: . Sometimes it is not possible. Then people write powers using the ^ sign: 2^3 means .
The number is called base, and the number is called exponent. For example, in , 2 is the base and 3 is the exponent.
To calculate a person must multiply the number 2 by itself 3 times. So . The result is . The equation could be read out loud in this way: 2 raised to the power of 3 equals 8.
- for every number x
- is the square of
- is the cube of
If the exponent is equal to -1 then the person must calculate the inverse of the base. So
If the exponent is an integer and is less than 0 then the person must invert the number and calculate the power. For example:
If the exponent is equal to then the result of exponentiation is the square root of the base. So Example:
Similarly, if the exponent is the result is the nth root, so:
If the exponent is a rational number , then the result is the qth root of the base raised to the power of p, so:
There are some rules which help to calculate powers:
- : Where the base is greater than 1 and the exponent is 0, the answer is 1. If the base and exponent are both 0, the answer is undefined.
It is possible to calculate exponentiation of matrices. The matrix must be square. For example: .