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 threefourths power, raise everything to the fourthirds power.
Check:
Intro Problem Revisit
We need to plug 156.8 in to the equation
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 threehalves 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