The period (in seconds) of a pendulum with a length of
(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.
= 9 is a solution to
and see if the equation holds.
9 is a solution to this equation.
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.
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
and solve. If our answer equals
, then the given length is correct.
does not equal
, so the length cannot be 156.8.
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.
Determine if the following values of
are solutions to the equation
Solve the following equations. Round any decimal answers to 2 decimal places.