# Examples of how to solve rational radical powers

Perhaps best, before addressing some of the cases that may serve as an example to the indicated way of finding what is the power of a rational radical, is to review the very definition of this operation, in order to understand each of the cases in its precise context.

## Power of a rational radical

In this sense, it must then begin by remembering that mathematical discipline has explained rational radicals as any root operation that counts as rooting a fraction, and that it must be resolved by finding out what fraction is rising to the number that the operation offers as an index, gives as potency the fraction that the root has as rooting. Consequently, a rational radical is also understood – as most authors point out – as an inverse expression to rational base power.

For its part, the Power of a rational radical may be described as a mathematical operation, by which it seeks to raise a certain number rational radical, in order to determine the product that is obtained from multiplying by itself this radical rations, as many times as dictated by a second numerical element, so it can also be said that the Power of Rational Radicals are abbreviated multiplications in which such expressions participate.

## Steps to solve the power of a rational radical

Likewise, the mathematical discipline has indicated what are the steps to be taken when solving such an operation, and which can basically be summarized in the following:

1. Since a rational radical is elevated to a specific exponent, it will be choose to elevate the radical’s establishment to this exponent, while the index will remain the same.
2. As the Mathematics indicates when solving a fractional power, the best way to do so will be to raise each element of the fraction – numerator and denominator – to the exponent given by the operation.

The way to solve such operations can also be represented mathematically as follows:

## Examples of rational radical powers

However, the best way to study this operation may be through the exposure of some examples, which allow us to see in practice how the steps indicated by mathematical theory are met. Here are some of them:

## Example 1

Resolve the following operation:

When solving this operation, it will then be necessary to start by elevating the establishment to the indicated exponent. Once done, seeing that the elements are squared, and that the radical has an index equal to 2, the fraction can leave the root:

## Example 2

Resolve the following operation:

As the theory dictates, in order to solve this operation, the fraction must be raised to the indicated exponent:

Seeing that the fraction cannot leave the root, if one wanted to express this as a power, then a rational exponent should be used:

## Example 3

Resolve the following operation:

At the time of solving this operation, the fraction should be raised to the negative exponent, remembering that these types of situations are solved by raising the inverse of the fraction to the same exponent but positive:

Having done this, you should then elevate each element of the operation to the designated exponent, which will lead you to see how each element can to see it exit the square root:

The fraction obtained is then considered as the response of the operation:

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Examples of how to solve rational radical powers
Source: Education
October 17, 2019