What is empowerment?

What Does empowerment Mean

Empowerment is a term related to the verb empower . This action, for its part, consists of providing power (strength, ability) to something. For example: "The coach sought the empowerment of his team with the incorporation of López and Sarachet" , "We have to invest in the empowerment of radio so we reach more listeners" , "The empowerment of the city as a tourist destination is one of the objectives of this government ” .

The most common use of the concept, however, is associated with mathematics . In this sense, empowerment consists of raising a number to a certain power . This operation is developed from the participation of a base and an exponent : the base is raised to the exponent.

Let's look at an example. The operation 3 raised to 4 consists of multiplying 4 times the number 3 by itself (which returns the result 81 ). In this case, 3 is the base and 4 is the exponent. This same logic can be applied to real numbers, complex numbers , and various kinds of algebraic structures . Empowerment has several properties, and some of them are fairly straightforward to understand compared to more complex operations.
If you have two or more powers of the same base , it is possible to replace them by a single one whose exponent is the total of the sum of the previous ones; for example: the product of 9 squared by 9 cubed by 9 to 5 is equivalent to raising 9 to 10 (this exponent is obtained by adding 2 + 3 + 5 ).
When the power of another power must be calculated, there is the possibility of simplifying the equation by multiplying the exponents of the powers and raising the base to the number that results from said product; for example: if you have 4 squared in parentheses, everything cubed, it is possible to replace the calculation by a single power, in which the base is 4 and the exponent is the result of multiplying 2 x 3 .
Another property of the potentiation says that in the power of a product, that is, when you want to raise a series of multiplied numbers enclosed in parentheses to the same exponent, it is possible to extract them and raise each one individually to said exponent, obtaining the same Outcome; For example, if we have in parentheses the product 4 x 9 x 5 , all squared, it is possible to obtain the same result if each base is squared and the parentheses are eliminated.

The division of powers of equal base, on the other hand, can be replaced by a single power whose exponent is equal to subtracting the exponent of the dividend from that of the divisor; for example: if you try to divide 4 cubed by 4 squared, the same result would be obtained by raising 4 to 1 (where 1 arises from the difference 3 - 2 ).
It is worth mentioning that the empowerment is not distributive when there are additions or subtractions raised to a common exponent; in other words, a group of additions or subtractions enclosed in parentheses and raised to a certain exponent cannot be extracted and expressed as separate powers, which is possible with multiplication (as explained above).
Empowerment can be translated to a graph from a parabola (when the exponent is natural and odd) or from a curve with linked branches at the vertex (if the exponent is natural, but even).
In some specific cases, the empowerment is read differently and not with the formula "raised to the number x" . If the number is raised to 2 , it is said to be “squared” while if the empowerment consists of raising to 3 , it is called “cubed” .

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