Rational and exponent-based powers 0

Perhaps the best thing, before addressing an explanation of how the Rational-Based and Zero-Exponent Powers should be resolved, is to revise in advance some definitions, which will allow us to understand this operation within its precise context.

Fundamental definitions

In this sense, it may then be necessary to delimit this theoretical revision to two specific notions: Power-up, Fractions and Rational-Based Powers, as these are mathematical operations and expressions, directly related to the implying that there is a rational number raised to zero (0). Here are each of these concepts:


In this way, it will begin by saying that the Mathematics has defined The Empoweror as an operation, whose main purpose is to determine which product is obtained from multiplying a number by itself, as many times as indicated by a second element therefore, some authors are inclined to point out the Poweralso as an abbreviated multiplication, which can be expressed in mathematical terms as follows:

an = an . an2  . an

As for the elements that constitute this operation, mathematics has also distinguished between three of them, each of which has been described as can be seen below:    

  • Base: it will be made up of the number to be multiplied by itself, as many times as indicated by the next number involved in the operation.
  • Exponent: for its part, the exponent will also consist of a number, and will point to the base how many times it must multiply on its own.
  • Power: Finally, the Power will be considered the product of the multiplication that has made the base by itself, the times that the exponent has indicated to it. That is, it is the final result or resolution of the operation.


It will also be necessary to review the concept of fractions, which may be understood, in the light of what the Mathematics indicates, as the expression by which it is aware of fractional amounts, that is, not exact or non-whole. Similarly, the mathematical discipline indicates that the fraction will consist of two elements, each of which has been explained in turn as follows:

  • Numerator: This is the element that makes up the top of the fraction. Your mission will be to indicate how many parts have been taken altogether.
  • Denominator: For its part, the denominator will be the element that occupies the bottom of the fraction, and that has the task of indicating how many parts the whole is divided.

Rational-based powers

Finally, the Rational Base Powers will be understood as those Power-Up operations that are based on a rational number or a fraction, and an exponent consisting of a natural number, i.e. a positive integer. Like any such operation, the Rational Base Powers will be solved by multiplying the base by itself so many times points to the exponent, which can be expressed mathematically as follows:

Rational and exponent-based powers 0

Once each of these definitions have been revised, it may be much easier to understand the mathematical property that operates on any rational-based fraction that is raised to zero (0), and that as is the case when the base is an integer will result in , always and without exception, the unit, i.e. 1. This property may be expressed in mathematical terms as follows:

Examples of rational and exponent base powers 0

However, it is likely that the most efficient way to complete an explanation of ownership that exists in terms of powers that have a fraction as a base, and have been raised to 0, is to present some examples that allow us to see in a concrete way how complies with this mathematical law without exception. Here are some of them:

Picture: pixabay.com

Rational and exponent-based powers 0
Source: Education  
September 30, 2019

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