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Perhaps the best thing, before delving into an explanation of mathematical property known as the whole-base integer power sachet, **is to briefly revise some definitions,** which will allow us to understand this Act within its context Mathematician.

## Fundamental concepts

However, it may also be prudent to delimit this revision to two specific notions: Integers and the Empowerment of integers, **since these constitute respectively the numerical elements and the mathematical operation** on the basis of the ownership of the Power Ratio of integers of equal basis. Here’s an explanation of each of them:

## Integers

Consequently, it will begin by saying that Integers are understood **by Mathematics as the elements on which the numerical set of the same name,** also called the Z set, is formed, **and where three elements will be found:**

**Positive integers:** First, positive Integers will be distinguished, which in turn make up the whole of natural numbers, ranking in the number line to the right of zero. They range from 1 to infinity. **Its membership in this set allows you to perform some mathematical tasks,** such as counting the elements of a set, assigning them a position or hierarchy, and also expressing accounting amounts with it.

**Negative integers:** On the other hand, negative integers will make up the second subset that can be within the Z set. **It is made up of numbers, which extend from -1 to -o, thus being located to the left of zero in the number line.** They are considered inverse of positive integers, while their membership in this collection makes it possible for them to realize the absence or lack of specific amounts.

Zero: finally, zero will also be considered part of the set Z. However, this element will not be taken as a number,** but as the total absence of quantity, being used then precisely to express this mathematical situation**. Because it is not a number, then it will be neither positive nor negative. He’s considered his own inverse.

Similarly, it should be noted that mathematics considers as an integer any numeric element – whether positive, negative or zero –** that serves to represent an exact numerical quantity.** It is therefore inferred that fractional numbers, or those with decimal expressions, **are thus unable to belong to this numerical collection.**

## Empowering whole numbers

This will also require a thrown of lights on the definition of The Empowering of Whole Numbers, **which has in turn been explained by Mathematics as that operation where an integer chooses to multiply by itself**, every time a number, which must also be strictly integer, resulting in a product. Similarly, some authors have pointed out that this operation may also be defined as an abbreviated multiplication.

As for its elements, the Mathematics indicates that these can be counted in three: the Base, consisting of an integer that will multiply by itself, the times the second number involved points to it; the Exponent, which is also an integer, will be responsible **for pointing out to the base how many times it must multiply on its own;** finally, the Power will be understood as the final result of the operation.

## Equally base integer power ratio

Bearing these operations in mind, it may then be much easier **to approach the explanation given by the Mathematics on property called The Same Base Integer Power Ratio**, which takes place in such operations, is to say, divisions constituted by powers where bases consisting of whole numbers are observed, which coincide in their value, and which according **to this Law must be resolved by assuming a single basis,** subtracting the values of their exponents, and then raising this base to the difference obtained between exponents.

**This property can be expressed mathematically as follows:**

a^{m} : a^{ n} = a^{m-n}

## Examples of whole-number power ratio of equal base

However, perhaps the most efficient way to complete an explanation about this mathematical property, **observed in terms of the potentiation of integers,** is through a specific example, such as the one shown below:

**Resolve the following operation:**

**-4 ^{6} : -4^{2} =**

When wanting to comply with the postulate of the financial year, it will be noted that the operation clearly constitutes a Division or power ratio of whole numbers of equal base, so the first step will be to assume a single base, and proceed to subtract the exponents:

**-4 ^{6} : -4^{2} = -4^{6-2}**

**-4 ^{6-2} = -4^{4}**

Once this step has been completed, the power base must then be raised to the difference obtained from the exponent subtraction, in order to obtain the final power:

**-4 ^{4}= 256**

In doing so, another mathematical law will be revealed in reference to the Empowerment of integers, **which indicates that whenever a power has a positive exponent,** regardless of whether its base is positive or negative, the result will be a positive integer.

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September 21, 2019