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?

### 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 .

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

Check:

#### 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.

Check:

**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.

2.

#### Answers

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

Check:

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.

Check:

### 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.