Power of a power in whole numbers

Probably the best way to address an explanation about the property called Power of a power in whole numbers, is to review some definitions, which will allow us to understand this Mathematical Law within its precise context.


Fundamental definitions

It may also be useful to focus this theoretical review on two specific notions: the definition of Integers and the Definition of Characterising Integers, as they are respectively the elements and the operation where this property takes place concerning the correct way to solve the power of a power, when set based on whole numbers. Here are each of these concepts:

Whole numbers

In this way, it will begin by saying that whole numbers have been explained by Mathematics as those numerical elements, representing whole and exact numerical amounts. Consequently, it is then inferred that within such numbers there is no place for those fractional numbers, or that they have some decimal expression.


Similarly, this discipline has pointed to the total of the Integers as the elements on which the eponymous set is established, or which is also known as the Z set, and where it has been noted that integers are in turn grouped two subsets and an element, defined as follows:

  • Positive integers: First, you will find those positive integers, which make up the set of Natural Numbers, this collection that is taken as a subset of Z. These numbers are located to the right of zero, in the number line, where you extend from 1 to infinity. Membership of positive integers to Z will make it possible for this set to express accounting amounts, or count the elements of a set.
  • Negative integers: On the other hand, negative integers will also make up one of the subsets found in Z. These numbers will be considered inverse to positive numbers. They will be located on the number line, to the left of zero, extending contrary from -1 to -o. His presence in this set will make it possible for him to express the absence of a certain amount.
  • Zero: Finally, zero will also be part of the elements found in the set of integers. It is not considered a number, but the absence of quantity. Consequently, it will be used to express this mathematical notion, while it will not be considered positive or negative. Similarly, the different sources point out that he should be considered inverse to himself.

Empowering whole numbers

In another order of ideas, it will also be necessary to bring to chapter the definition promulgated by the Mathematics on the Empowerment of whole numbers, being then described as a mathematical operation, set strictly between whole numbers, and where one of these numbers – called Base – chooses to multiply itself, as many times as a second number indicates – which will be called Exponent – in order to obtain a result or product – which will be called Power.

Power of a power in whole numbers

Once these definitions have been specified, it may certainly be much easier to approach an explanation of ownership that mathematics has indicated on the power of a power, when the numbers involved are integers.

In this sense, this discipline then points out that whenever an operation is facing integers, where you want to calculate the power of a power, you must assume a single base, while the exponent of the power is multiplied they go to each other, to subsequently raise the base to the product obtained in multiplication, obtaining the power or final result, which can be expressed mathematically as follows:

Example of Power of a power in whole numbers

However, perhaps the most efficient way to complete an explanation of this mathematical property, whether by exposing a particular example, such as the one shown below:

Picture: pixabay.com

Power of a power in whole numbers
Source: Education  
September 18, 2019


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