To express a rational radical as a power

Perhaps most convenient, before delving into an explanation of how a rational radical should be expressed in the form of a power is to address some concepts, which will allow us to understand this operation in its precise mathematical context.

Fundamental definitions

In this regard, it may also be prudent to focus this conceptual review on four specific notions: Fractions, Radication, Rational Radicals, and Empowerment, as these are the expressions and operations directly related to the procedure by which an operation raised in terms of establishment can be shown as a power. Here are each of these definitions:


In this way, the concept of fractions, which has been explained by Mathematics as a type of expression through which it is aware of rational or fractional numbers, that is, that fractions will be used to represent non-whole or non-exact amounts. Likewise, the different authors point out that Fractions will also be understood as expressions composed of two elements, explained in turn as follows:

  • Numerator: on the one hand, the Numerator will be the numerical element that occupies the top of this expression, taking charge to indicate how many parts of the whole have been taken.
  • Denominator: In the second instance, the Denominator will constitute the lower element of the fraction. Its task is to indicate in how many parts the whole is divided, of which the fraction, through the Numerator represents only a few, or sometimes also all.


Thus, it will also be necessary to cast lights on the definition of Radicación, understood by its part as a mathematical operation, whose main purpose is to determine what is the number, which being raised to the index, which the operation initially proposes, gives as result the establishment that this also offers from the beginning.

Consequently, some authors understand the Radication as a reverse expression of the Empoweror, since if it were raised in these terms, it would be trying to find the basis, corresponding to the power (radical).

Rational radicals

Thirdly, it will also be appropriate to take a moment to review the definition of Rational Radicals, which have been explained as mathematical expressions composed of a coefficient and a numerical element, enlammed by a radical sign, which always and without exception consists of a fraction or rational number. That is, a rational Radical will be a root that always has as if a fraction is in place. The correct way to resolve such operations will be by calculating the root of each element of the fraction separately.


Finally, it will be useful to also call the chapter the definition of Empowerion, which has been seen as the operation by which it seeks to determine what is the product of multiplying a number (which serves as the basis) as many times as a second indicates element (used as an exponent) fact that leads to affirm, taking the floor of some authors, that the Empoweror can also be described as an abbreviated multiplication.

Express ingestana root in the form of power

Once each of these concepts has been revised, it may be much easier to approach an explanation of how another rational radical can express itself, and that the root being an inverse operation to empowering, there can be no other option of expression to the root that powers.

Therefore, whenever it is necessary to express the Rational Radical in the form of Power, the root index should be placed as the denominator of the exponent to which the Rational Radical is elevated. If this is not explicitly stated, it will be assumed to be equivalent to the unit. This procedure can be expressed mathematically by talking as follows:

Example of how to express a Root in the form of power

However, perhaps the best way to complete an explanation of how any rational Radical should be exposed in the form of a power-up is through the presentation of a particular example, which allows us to see in a practical way how each one is met related to the application of this procedure, as can be seen below:

Express in the form of empowering the following rational radical:

To do this, you must then take the index of the radical, and place it as the denominator of the exponent:

To express a rational radical as a power
Source: Education  
September 30, 2019

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