Integer powers with zero exponent

The Mathematician

Integer powers with zero exponent

The Mathematician Before delving into mathematical property concerning the powers of integers, which have exponent...

Before delving into mathematical property concerning the powers of integers, which have exponents equal to zero, it may be best to consider some definitions, which will be necessary when understanding this mathematical law within your precise context.

Fundamental definitions

However, it may be prudent to also focus this theoretical review on two basic concepts: in this way,the definition of Whole Numbers, as well as the definition of Empowerment in whole numbers, will then be studied, as these are the numerical elements and the operation on the basis of which this mathematical property arises. Here’s each one:

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Whole numbers

First, as most authors point out, those numerical elements, used to represent exact quantities, will be known as integers, which then leaves fractional numbers out of this denomination, or those that they have decimal expressions of some kind.

On the other hand, the different theoretical sources also state that whole numbers may be defined as those elements that constitute the numerical set of the same name, which is also known as the Z set, and where several distinguished are distinguished subsets, consisting of groupings of integers, explained in turn by mathematics as follows:

Positive integers: First, you will find all positive integers, located in the numerical line to the right of zero, region where they extend from 1 to infinity. These numbers in turn make up the set of Natural Numbers, this collection which will then also be subset of Z. Through these numbers, this set can be used to express accounting quantities, or count the elements of a grouping.

Negative integers: Identified as another of the subsets that make up the Z set, these numbers will be located to the left of zero in the number line, being considered inverse of negative integers, as well as elements that can be used each time you want to give reason for the absence or debt of an exact amount. They are always distinguished to be accompanied by the minus sign (-) with which they show their negative character.

Zero: Finally, zero will constitute an element belonging to the Z set. However, this is not understood as a number, but as a total absence of quantity, a mathematical situation that is then expressed with this element. Thus, as a consequence of not being understood as a number, zero will not be positive or negative, while then assuming itself as inverse of itself.

Power of whole numbers

Similarly, it will be appropriate to revise the definition of Absorption of integers, which has been explained in general by the different sources as a mathematical operation in which a given whole number must multiply by itself, so many as you are given a second number, which must also and necessarily belong to the whole of the Whole Numbers.

The number that multiplies itself will receive the base name, while the number that tells you how many times it should be multiplied by itself will be called an exponent. The result or product of this abbreviated multiplication – a definition by which the power is also explained – will receive the power designation.

Integer powers with zero exponent

Once these definitions have been revised, it may then be much easier to approach the mathematical property over those integer powers that have zero-equivalent exponents. In this sense, it will then be said that most authors agree that whenever in a potentiation established based on whole numbers, regardless of the whole number that serves as the basis, provided that it is raised to an exponent equal to zero, will result in one (1) which can be expressed mathematically as follows:

a0 = 1

Examples of Integer Powers with zero exponent

However, it may also be necessary to provide some examples that allow us to see in a practical way how every whole number that is raised to an exponent equal to zero, generates a power equal to 1, as can be seen in the examples below :

230 = 1
-20 = 1
1000 = 1
-540 = 1
88000 = 1


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Bibliography ► (September 18, 2019). Integer powers with zero exponent. Recovered from

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