Potentiation (exponentiation): what it is and properties of potencies

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THE potentiation or exponentiation is the mathematical operation that represents the multiplication of equal factors. That is, we use potentiation when a number is multiplied by itself several times.

To write a number in the form of potentiation we use the following notation:

If a ≠ 0, we have:

a: Base (number being multiplied by itself)
n: Exponent (number of times the number is multiplied)

To better understand the enhancement, in the case of number 2³ (two to the third power or two to the cube), we have:

2³ = 2 x 2 x 2 = 4 x 2 = 8

Being,

2: Base
3: Exponent
8: Power (product result)

Potentiation Examples

5²: reads 5 to the second power or 5 to the square, hence:

5 x 5 = 25

Soon,

The expression 5²equals 25.

3³: reads 3 to the third power or 3 to the cube, hence:

3 x 3 x 3 = 27

Soon,

The expression 3³equals 27.

Potentiation Properties

Every power with an exponent equal to zero, the result will be 1, for example: 5⁰=1
Every power with an exponent equal to 1, the result will be the base itself, for example: 8¹ = 8

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When the base is negative and the exponent is an odd number, the result will be negative, for example: (- 3)³ = (- 3) x (- 3) x (- 3) = - 27.
When the base is negative and the exponent is an even number, the result will be positive, for example: (- 2)² = (-2) x (-2) = +4
When the exponent is negative, the base is inverted and the sign of the exponent is changed to positive, for example: (2)^{- 4} = (1/2)⁴ = 1/16
In fractions, both the numerator and denominator are raised to the exponent, for example: (2/3)³ = (2³ / 3³) = 8/27