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• MCR3UUnit4:ExponentialRelationsLesson1 Date:___________Learninggoal:Icansimplifyandevaluateexpressionsinvolvingnegativeandrationalexpressionsusingexponentlaws.

ExponentLaws

POWERS

Powersareaconvenientwayofwritingrepeatedmultiplication.

Apowerconsistsoftwoparts:

1. Abasetellsuswhichvaluetorepeatedlymultiply,and

2. Anexponenttellsushowmanytimestoperformthemultiplication.

!!

Thepowercanbewritteninexponentialformas34,inexpandedformas(3)(3)(3)(3),orevaluatedformas8.

Recallthedifferencebetweennegativebasesandcoefficients.

3 ! = 3 3 = 9,but3! = 3 3 = 9.

EXPONENTIALLAWS

Example1:Simplifythefollowing.

a)(5!!!!!!)(2!!!!!!) b)(3!!!!)! c) (!"!!!!!!!!!!!!!!)!

ExponentLaw

!!!! = !!!! !!

!! = !!!!, ! 0

!" ! = !!!! !!!= !

!

!! , ! 0

!! ! = !mn !! = 1

!!

!!= !! ,!, ! 0

!!

!!= !!

!,!, ! 0

• d)(!!!!! )!! e)(!!!

!!!!!)(!!!!!!!!)!!"!!!!! f)

(!!!!!!)!!(!!!!!)!(!!!!!!!)!!

g) 3!(3!! 3!!!!) h)!!!!!!!!!! RATIONALEXPONENTS

Example2:Useacalculatortocompletethefollowing.

a) 9!! =and 9 =

b) 64!! =and 64! =

c) 16!! =and 16! =

RationalExponents

1. !!! = !! (if! > 1and! 0)!! iscalledaradicalandmeansthenthrootofb.

2. !!! = !!! !!or!

!! = !!!

(ifmandnarebothpositiveintegersand! 0)

a) !!!

b) !!! c) 125!

!!

Example4:Writeeachexpressionasapowerusingrationalexponents.Donotevaluate.a) 12!

b) ( 13! )! c) !!! ( !!! )

a) 64!!

b) ( !"!"#)!! c) (!"!")

!!!

d) (32)!!!

e) 125!!! f) 16!.!"

• g) (9!!9

!!)!"

h) 64! i) ( 5!! )( 5! )

HW:Pg.79#1-4withoutcalculator,14,16,17,pg.85#1-6,13,14(#5cans !!! )

SuccessCriteriatoEvaluatingPowerswithRationalExponents!!!

1.

2.

3.

4.

2 5 = 25= 10

Ingeneral ! ! = !!

102

= 2 52 = 5

Ingeneral !! =!!

a)2 50 b)9 24 14 c) !"!"

d)!!" !"#! ! e)!"! !"

! f)!!"!! !"#

!

a)10 2 7 3 + 2 2 + 4 3 b) 24 + 54 + 150 c) 3 48 4 8 + 4 27 2 72

• RATIONALIZINGDENOMINATORS

Example3:

a)! !! b)! !! ! c)

!! 72!

Example4:Simplify.

a) !! !! ! b)! !! !! !!! !

HW:Simplifying&RationalizingWorksheet

• Simplifying&RationalizingWorksheet

1. Simplify.a)4 75 2 12 + 8 48 2 8 b)3 63 + 88 2 112 c)!!! !"!"

2. Rationalizethedenominatorforeachofthefollowing:

a) !! b)!! c)

!! !!! ! d)

! !!! !!! !

e)!!! !!! ! f)!

!!!!! g)!10

!! !!!

3. Simplify.

a)! !! b)! !! !

! c)!

10!! d)! !

! !!!

e) !! !!! ! f)!

! 27!! 12 g)!!!

! 27!! !

1a) 48 3 4 2 b) 13 7+ 2 22 c)!!! !! 2a)! !! b)

!! c)5 2 6 d)

16!! 10! e)

!10! !! !!! 15! f)

!!!!!!!! g)2 ! + 5+ !

3a) 21 b)3 3 c) !! !! d)12!! !

! e)!! 21! f)

!13 g)

!! !!! !!! !!

• MCR3UUnit4:ExponentialRelationsLesson3 Date:___________Learninggoal:Icansolveequationswithavariableintheexponent.

SolvingExponentialEquations

RECALL: 2! 3! cantbesimplifiedthroughlaws.Powerlawsonlyapplyifbasesarethesame.However,sometimesbasescanbechanged.

3! 9! = 3! 3! !

= 3! 3!= 3!

Example1:Writethefollowingpowerswithabaseof2.

a)!! b)4!! c) !16

!

SOLVINGEXPONENTIALEQUAITONSExponentialequationshaveunknownsintheexponent.Example2:Solve.

a)9!!! = 3!!! b)25!!!! = ( !!"#)! c) 2!!!! = 8

SuccessCriteriaforSolvingExponentialEquations

1. Writeexpressionsaspowersofthesamebase.

2. Dropthebase,settheexponentsequaltooneanother

3. Solve

• d) 2 !!! ! = 64 e) 4 7!!!! = 1372 f) 9! + 3! = 12

HW:Pg.94#1,4,6-9,13,22-24