Fractional Exponents

Intro

Previously, we have worked with powers that were integers.  In this tutorial, we wish to consider powers that are fractions.  There are two ways to write expressions with fractional powers:   

In the tutorial on Laws of Exponents, we learned the following law:

(ab)c =ab*c

 

This law will allow us to determine the value of expressions with fractional exponents.

Examples

Example 1: 

Find the value of

Solution:

Step 1:  Create a solvable equation

Step 2:  Solve the equation:

Note:   You should have noticed that is the same as the square root function,, with which we are already familiar

 

 

 

Example 2: 

Find the value of

Solution:

Step 1:  Create a solvable equation

Step 2:  Solve the equation:


Example 3: 

Find the value of

Solution:

Step 1:  Create a solvable equation

Step 2:  Solve the equation:


 

 

Generalization

The expression  satisfies the equation:

 

Practice with numerators equal to 1:

Click below to practice

 

 

 

Numerators other than 1

We know now how to manage expressions of the form fractional powers:  .  To deal with fractional exponents of the form , we  again use the law

 (ab)c =ab*c

 

This law allows us to rewrite the expression as .

Example 1: 

Find the value of

Solution:

Step 1:  Create a solvable equation for

Step 2:  Solve the equation :

 

Step 2:  Solve the equation

 

 

Example 2: 

Find the value of

Solution:

Step 1:  Create a solvable equation for

Step 2:  Solve the equation for :

Step 3:  Solve the equation for :

 


Example 3: 

Find the value of

Solution:

Step 1:  Create a solvable equation

Step 2:  Solve the equation for :

Step 3:  Solve the equation for :

 

Practice with numerators not equal to 1:

Click below to practice