Fractional Exponents

The following diagram shows how to evaluate fractional exponents. Scroll down the page for more examples and solutions.

 

How to evaluate fractional exponents?

In this lesson, we will consider xⁿ, where n is a fraction and x is an integer.

Let us first consider fractional exponents of the form:

In general, we define:

A number x is the n^th root of a number y if xⁿ = y.

Example:

Evaluate the following:

Solution:

We will now consider fractional exponents of the form:

In general, we define:

 

Example:

Evaluate the following:

 

Solution:

 

The following video gives more examples of fractional exponents

• Show Step-by-step Solutions

Evaluating Numbers Raised to Fractional Exponents

• Show Step-by-step Solutions

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