Power ratio with equal base numbers

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:


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:

am :  a n =  am-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:

-46 : -42 =

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:

-46 : -42 = -46-2

-46-2 = -44

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:

-44= 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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Power ratio with equal base numbers
Source: Education  
September 21, 2019

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