Potentiation is an operation that consists of raising a number to a certain power.
Potentiation is a term related to the verb enhance . This action, for its part, consists of providing power (strength, capacity) to something.
For example: “The coach sought to strengthen his team with the additions of López and Sarachet,” “We have to invest in strengthening the radio so we can reach more listeners,” “The strengthening of the city as a tourist destination is one of the objectives of this government.”
Strengthening in mathematics
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 to the power of 4 consists of multiplying the number 3 by itself 4 times (which returns the result 81 ). In this case, 3 is the base and 4 is the exponent. This same logic can be applied with real numbers , complex numbers , and various kinds of algebraic structures . Potentiation has several properties, and some of them are quite simple to understand compared to more complex operations.
In potentiation, the base is raised to the exponent.
Operation properties
If you have two or more powers with the same base , it is possible to replace them with 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 the power of 5 is equivalent to raising 9 to the power of 10 (said 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 resulting from said product; For example: if you have 4 squared in parentheses, all cubed, it is possible to replace the calculation with a single power, in which the base is 4 and the exponent results from multiplying 2 x 3 .
Another property of potentiation says that in the power of a product, that is, when you want to raise a series of numbers multiplied together enclosed in parentheses to the same exponent, it is possible to extract them and raise each one individually to said exponent, obtaining the same result; For example, if we have the product 4 x 9 x 5 in parentheses, 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 the power of 1 (where 1 arises from the difference 3 – 2 ).
It is worth mentioning that 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).
Boost graph and reading
Potentiation can be transferred to a graph from a parabola (when the exponent is natural and odd) or from a curve with branches linked 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 raised “squared” while if the potentiation consists of raising it to 3 , it is said to be raised “cubed” .