Exponentiation - Simple English Wikipedia, the free encyclopedia

# Exponentiation

### From Simple English Wikipedia, the free encyclopedia

Exponentiation (power) is something which is done on numbers. It is repeated multiplication. You write exponentiation with upper index. This looks like this: xy. Sometimes (e.g. if you write e-mails) it is not possible. Then people write powers using `^` sign: `2^3` means 23.

The number x is called base, and the number y is called exponent. For example, in 23, 2 is the base and 3 is the exponent.

To calculate 23 you must multiply 3 times the number 2. So . The result is .

Examples:

- 1x = 1 for every number x

If the exponent is equal to 2, then the power is called square because the area of a square is calculated using a2. So x2 is the square of x.

If the exponent is equal to 3, then the power is called cube because the volume of a cube is calculated using a3. So x3 is the cube of x.

If the exponent is equal to -1 then you must calculate the inverse of the base. So . If the exponent is an integer and is lesser than 0 then you must invert the number and calculate the power. For example: .

If the exponent is equal to 1/2 then you must calculate the square root of the base. So . Example: .

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: .

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Category: Mathematics

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