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

### Solving Rational Exponent Equations

When solving a rational exponent equation, you first isolate the variable. Then, to eliminate the exponent, you will need to raise everything to the reciprocal power.

Let's determine if *x* = 9 is a solution to

Substitute in *x* and see if the equation holds.

9 is a solution to this equation.

Now, let's solve the following equations for x.

3x52=96

First, divide both sides by 3 to isolate

Check:

−2(x−5)34+48=−202

Isolate

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

Check:

### Examples

#### Example 1

Earlier, you were asked to verify the length of the pendulum.

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

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

#### Example 2

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

Check:

#### Example 3

Here, only the

Check:

### Review

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 Review Problems

To see the Review answers, open this PDF file and look for section 7.9.