<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation

Solving Equations with Fractional Exponents

Raise fractional exponents to their inverse power to cancel

Atoms Practice
Estimated7 minsto complete
Practice Solving Equations with Fractional Exponents
Estimated7 minsto complete
Practice Now
Solving Rational Exponent Equations

The period (in seconds) of a pendulum with a length of L (in meters) is given by the formula . If the period of a pendulum is is the length of the pendulum 156.8?


This concept is very similar to the previous two. When solving a rational exponent equation, isolate the variable. Then, to eliminate the exponent, you will need to raise everything to the reciprocal power.

Example A

Determine if x = 9 is a solution to .

Solution: Substitute in x and see if the equation holds.

9 is a solution to this equation.

Example B

Solve .

Solution: First, divide both sides by 3 to isolate .

is raised to the five-halves power. To cancel out this exponent, we need to raise everything to the two-fifths power.


Example C

Solve .

Solution: Isolate by subtracting 48 and dividing by -2.

To undo the three-fourths power, raise everything to the four-thirds power.


Intro Problem Revisit We need to plug 156.8 in to the equation for L and solve. If our answer equals , then the given length is correct.

does not equal , so the length cannot be 156.8.

Guided Practice

Solve the following rational exponent equations and check for extraneous solutions.




1. Divide both sides by 8 and raise everything to the three-halves power.


2. Here, only the is raised to the three-halves power. Subtract 141 from both sides and divide by 6. Then, eliminate the exponent by raising both sides to the two-thirds power.


Explore More

Determine if the following values of x are solutions to the equation

Solve the following equations. Round any decimal answers to 2 decimal places.

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 7.9. 

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Solving Equations with Fractional Exponents.


Please wait...
Please wait...

Original text