Perhaps it is best to move forward on the definition and other aspects of the **Property observed by mathematics in reference to the powers of integers with exponent one** (1), is to revise some definitions, which will allow us to understand this law within its precise context.

## Fundamental definitions

In this sense, it may also be prudent to delimit this revision to two specific notions: the concept of Integers and the concept of Empowering Integers, **because these are the elements and the operation,** on the basis of which this mathematical property takes place. **Here’s each one:**

## Integers

Consequently, you can begin by saying that Mathematics has been given to the task of defining integers as those numerical elements, **used to represent whole and exact amounts,** that is, that they are not supported those those fractional numbers or with decimal expressions.

Likewise, integers are understood as the elements that make up the numeric set that bears the same name,** or which is also known as the Z set, and in which three elements can be distinguished,** each with its own functions within es collection, and which in turn have the following description:

**Positive integers:** **First, the Z set will count among one of its subsets with positive integers,** numbers which in turn will make up the set of natural numbers. **These numbers are located in the number line to the right of zero,** extend from 1 to infinity, and fulfill the function of counting the elements of a set, or express accounting quantities.

**Negative integers:** These numbers are the second subset that can be found in the Z set. Its location in the number line, is located on the left side of the zero, similarly they are understood as inverses of positive integers. They fulfill the function of expressing the absence or lack of a specific amount.

**Zero:** Finally, zero (0) is also seen as an element of the Z set. However, it is not understood as a number, but as the total absence of quantity, **mathematical situation for which it will be used.** Thus, because it is not considered a number, zero (0) is not positive or negative, and also taken as inverse of itself.

## Empowerment

In another order of ideas,** it will also be necessary to review the Empowerion in whole numbers,** which will be understood as a mathematical operation in which a specific whole number multiplies itself, **as many times as indicated by a second number, which must also be whole**, hence the Empowering of integers is also seen by some authors as an abbreviated multiplication.

## Integer powers with exponent one

With these definitions in mind, it may certainly be much easier to approach the mathematical property dictated by those integer potentiation operations, **where an exponent equivalent to one (1) takes place.** In this sense, mathematical discipline points out that whenever this situation arises, regardless of the whole number that serves as the basis, the power or result obtained will be equal to the whole number that has functioned as a basis,** which in turn can be expressed mathematically as follows:**

## a1 to

## Examples of integer powers with exponent one

However, perhaps the most efficient way to close an explanation about this mathematical property inherent in potentiation with integers, whether through the exposure of an example, where you can see in practice how over and over again, whatever the basis , the result obtained when the exponent is one will be an **equivalent number to the one used as the basis, as will be seen in the exercises given below:**

3

^{1}= 3

-24^{1}= -24

5^{1}= 5

10^{1}= 10

-66^{1}= -66

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September 18, 2019