Skip Navigation

Fractional Exponents

Relate fractional exponents to nth roots

Atoms Practice
Estimated5 minsto complete
Practice Fractional Exponents
This indicates how strong in your memory this concept is
Estimated5 minsto complete
Practice Now
Turn In
Fractional Exponents

Suppose you want to find the cube root of a number, but your calculator only allows you to find square roots. However, it does allow you to find a number raised to any power, including non-integer powers. What would you do? Is there a way that you could rewrite the cube root of a number with a fractional exponent so that you could use your calculator to find the answer?

Fractional Exponents

The next objective is to be able to use fractions as exponents in an expression.

You can write roots as fractional exponents using the rule .

Let's simplify the following expressions by writing them without a root:



Evaluating Expressions with Exponents

It is important when evaluating expressions that you remember the Order of Operations. Evaluate what is inside the parentheses, then evaluate the exponents, then perform multiplication/division from left to right, and then perform addition/subtraction from left to right.

Let's evaluate the following expression:


Example 1

Earlier, you were asked how you can write the cube root so that you can use your calculator to find cube root of a number. 

As shown in this concept, you can write a root as a fractional exponent where the denominator is the power of the root and the numerator is the power that is inside the root. 

A cube root can be written as the number to the  power. 


Example 2

Simplify .

We start by simplifying using the fact that .

Next we rearrange knowing that 6 and 2 have a common factor, 2.


Simplify the following expressions. Be sure the final answer includes only positive exponents.

Simplify the following expressions without any fractions in the answer.

Evaluate the following expressions to a single number.

Mixed Review

  1. A quiz has ten questions: 7 true/false and 3 multiple choice. The multiple choice questions each have four options. How many ways can the test be answered?
  2. Simplify .
  3. Simplify .
  4. Simplify .
  5. Solve for .

Review (Answers)

To view the Review answers, open this PDF file and look for section 8.4. 

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Fractional Exponents.
Please wait...
Please wait...