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GUIDED NOTES – Lesson 4-4 Solving Fractional Exponent Equations Name: ______________________ Period: ___ OBJECTIVE: I can solve equations with fractional exponents, checking for valid vs. extraneous solutions.Remember that radical expressions can be represented with rational/fractional exponents (and vice versa).Examples: x=x3x2 =81/3 = =-18415238760Method 1:1) Isolate the power2) Raise both sides to the reciprocal power to cancel.3) Solve4) Check your answer020000Method 1:1) Isolate the power2) Raise both sides to the reciprocal power to cancel.3) Solve4) Check your answer4091379237325Method 2:1) Convert to root form2) Isolate the root3) Raise the appropriate power4) Take the root of both sides5) Solve6) Check your answer4000020000Method 2:1) Convert to root form2) Isolate the root3) Raise the appropriate power4) Take the root of both sides5) Solve6) Check your answerNow we will work on solving equations containing fractional exponents within them. Method 1 is simply dealing with the equation in its original fractional power form. Method 2 is essentially converting to root/radical form and doing the same solving as we did in the previous lesson. Reviewing reciprocals is necessary before we start. If one side of the equation is raised to a certain fractional power, raising both sides to the reciprocal power will ‘unlock’ that side.Examples: 12 reciprocal 23 reciprocal 43 reciprocal Example A:Example B:Example C:3x-112=2x+51235x-112-2=?03x+213+1=0Example D:Example E:3x+113=-532x+614-6=?0Almost got it! But here are some problems where the fractional power does not have a numerator of 1. Use the ______________ still, then remember some of the skills we developed in lesson 4-1, to help simplify when necessary.385 =293 =Example F:Example G:4x32-8=0x-123=64Example H:Example I:43x+523=?1003x+234+6=30APPLICATION 1: A formula used to determine the velocity v, in feet per second of an object after it has fallen a certain distance is: v= 2gd where g is the acceleration due to gravity and d is the distance the object has fallen. On Earth, the acceleration (g) due to gravity is approximately 32 feet per second.If you were to jump off a 15 foot diving board, how fast would you be falling as you entered the water?An object is dropped from an upper story window and passes a lower window with a speed radar gun. It clocks in at 90 feet per second. What must the distance be between the upper and lower window (how far had it fallen)?A loaf of French bread is dropped from the highest standing deck of the Eiffel Tower (896 feet up). What will the speed of the bread be when it hits the ground?APPLICATION 2: The Pittsburgh Steelers have a new field painter named Payton. He has a fresh bucket of white paint that says it will cover an area of 500 square feet.He knows from attending the University of Tennessee that the area of a circle is A=πr2493395079720500There is a backup painter on the sidelines waiting to take his job so he thinks “Go big or go home.” He stakes a rope in the center of the field and measures where to attach the black paint sprayer. What radius should he make the circle of their logo to use up all the white paint? ................
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