Fractional Exponents


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

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:

Text Box:  		(the nth root of a)

A number x is the nth root of a number y if xn = y.

Example:

Evaluate the following:

Text Box: a)  			b)    c)  			d)

Solution:

Text Box: a)  = 3		b)    c)  		d)



We will now consider fractional exponents of the form:

In general, we define:


 

Example:

Evaluate the following:

Text Box: a)      b)
 

Solution:

Text Box: a) Method 1:        Method 2:      b)
 

The following video gives more examples of fractional exponents

Evaluating Numbers Raised to Fractional Exponents



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