Exponentiation

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Exponentiation (power) is something which is done on numbers. It is repeated multiplication. You write exponentiation with upper index. This looks like this: x^y. 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: 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:

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• 1^x = 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:

It is possible to calculate exponentiation of matrices. The matrix must be square. For example: .

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