# 7.9: Solving Rational Exponent Equations

**At Grade**Created by: CK-12

**Practice**Solving Equations with Fractional Exponents

The period (in seconds) of a pendulum with a length of *L* (in meters) is given by the formula

### Guidance

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

Check:

#### Example C

Solve

**Solution:** Isolate

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

Check:

**Intro Problem Revisit** We need to plug 156.8 in to the equation *L* and solve. If our answer equals

### Guided Practice

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

1.

2.

#### Answers

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

Check:

2. Here, only the

Check:

### Explore More

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

x=32 x=−32 x=8

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

2x32=54 3x13+5=17 (7x−3)25=4 (4x+5)12=x−4 x52=16x12 (5x+7)35=8 5x23=45 (7x−8)23=4(x−5)23 7x37+9=65 4997=5x32−3 2x34=686 x3=(4x−3)32

### Answers for Explore More Problems

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

### Image Attributions

## Description

## Learning Objectives

Here you'll learn how to solve equations where the variable has a rational exponent.

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## Date Created:

Mar 12, 2013## Last Modified:

Jun 04, 2015## Vocabulary

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