Power of a radical

Perhaps the best thing, prior to addressing an explanation of the Power of a rational radical, is to briefly revise some definitions, which will allow us to understand this operation in its precise context.

Fundamental definitions

In this sense, it may be best to also delimit this conceptual review to four basic notions: Fractions, Empowerment, Radiation and Rational Radical, as these are the expressions and operations directly related to the procedure by means of which the Power of a rational radical is established. Here are each of these concepts:


In this way, it will begin to say that the Mathematics has conceived fractions as a mathematical expression, by means of which it is aware of rational or fractional numbers, ergo, this expression will serve to represent amounts not accurate or non-whole. On the other hand, Mathematics also indicates that fractions will always be made up of two elements, defined in turn as follows:

  • Numerator: First, the Numerator will be explained as the element or number that constitutes the top of the expression. Your mission will be to indicate how many parts have been taken altogether.
  • Denominator: On the other hand, the Denominator will be located at the bottom of the fraction. It has the task of pointing out how many parts the whole is divided into.


Thus it will also be necessary to address the definition of Empowerion, which is seen as a mathematical operation, whose main purpose is to determine what is the resulting product of multiplying for itself a number that makes the basis, so often points to a according to numerical element, which is an exponent, so it can then be said that The Empoweror can also be seen as an abbreviated multiplication.


As for the Radiation, the different sources have pointed out that it can be understood as a mathematical operation by which it is a question of calculating what is the number that being raised by the index originally offered by the operation results in the this procedure also initially indicates. Consequently, most sources agree that the Radiation can also be understood as a reverse expression of the Empoweror.

Types of adverbs based on their function

Finally, rational radicals can be explained – according to what they point to mathematical sources – as a type of mathematical expression, composed of a coefficient and a radical, which has a settlement consisting of a rational number or a Fraction. The correct way to resolve this operation or expression will be by calculating the radical of each of the elements that constitute the rational expression.

Power of a rational radical

Once each of these concepts have been revised, it may be much easier to address the notion of Power of a rational radical, which is understood as the operation by which it is sought to determine what is the product of multiplying for itself a radical reason as many times as the number that serves as an exponent points out.

Likewise, the Mathematics points out that whenever one wants to solve the Power of a rational radical it will be necessary to elevate the exponent only the radicay, without the index of the radical suffering any alteration. In this order of ideas it will also be important to point out that the correct way to solve the power of a rational, will be to elevate to the exponent each of the elements of this.

The Power operation of a rational radical may be expressed mathematically as follows:

Example of how to solve the Power of a rational radical

However, the best way to solve an operation where the Power of a rational radical needs to be calculated may be through the exposure of a particular example where you can see how each of the steps that warrant the solution of an ope such a ration, such as the following:

Resolve the following operation:

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Power of a radical
Source: Education  
September 30, 2019

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