Laws of Exponents

1 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-9 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONLaws of ExponentsAddition of ExponentsIf:a 0,a m a n = a m+nExample:23 22=(2 2 2) (2 2)=2 2 2 2 2=25=23+231 35=?PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-10 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONA nother Example For Negative Exponents2-3 2-2=123 122 ==123 22=123+2=125=2-5=2-3+-23-1 3-4=?PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-11 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONS till More Examples23 2-2=23+( 2)=21=2 Why?

2 23 2-2=23 122=2322=2 2 22 2=2 22 2 2=1 2 = 2 = 21 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-12 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONMore ExponentsIf a 0 aman = am-nExample:2723=2 2 2 2 2 2 22 2 2=2 2 22 2 2 2 2 2 2=1 24=24 (=16)So,2723=27-3 = 24 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-13 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONMore ExponentsExample:3235=3 33 3 3 3 3=3 33 3 13 3 3=1 133=3-3 =133=127 So,3235=32-5 = 3-3 Example:4545=4 4 4 4 44 4 4 4 4=1So,4545=45-5=40 = 1 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-14 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONIf a and b are not zero,(ab )n = a n b nExample:(3 5)4=(3 5) (3 5) (3 5) (3 5)=3 3 3 3 5 5 5 5=34 54 (= 81 x 625 = 50,625)Example:(2 5)3=(2 5) (2 5) (2 5)=2 2 2 5 5 5=23 53 (= 1,000)Note that (2 5)3 = 103 = 1,000So we have just "factored" 1,000 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-15 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONab n=anbnExample:35 4 = 35 35 35 35=3454 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-16 1999, CISC.

3 Curriculum and Instruction Steering Committee The WINNING EQUATIONIf a 0 (a m)n = a mnExample:(23)4=23 23 23 23=23+3+3+3 = 23 4=212 (= 4096)Example:13 2 3=13 13 3=13 13 13 13 13 13 =13 6 =1729 So,13 2 3=13 2x3=13 6 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsH-16 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONP racticeSimplify each expression (you may leaveanswers in exponential form.)a)23 28b)25 4 5c)5654d)23 32e)x20x20f)7-2 7-4g)(24) 7h)30i)(x2y) 4 Challenge:j)12 3 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-17 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONA nswers to Practice Problemsa)23 28=23+8=211b)25 4 5=2454 51=2453c)5654=56 4=52 = 25d)23 32=23 32 (bases are different)e)x20x20=x20 20=x0=1f)7 2 7 4=7 2+ 4=7 6=176g)24()7=228h)30=1i)x2 y()4=x8y4j)12 3=(2 1) 3=2 1 3=23=8 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-18 1999, CISC.

4 Curriculum and Instruction Steering Committee The WINNING EQUATIOND efinitions Square root - a number that when multiplied byitself produces a given :3 is a square root of is also a square root of 9. Radical Sign The symbol for the positivesquare convention, the radical sign, a designatesonly the positive square Sign 36 RadicandPRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-19 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONS quaring and Taking a Square Rootare Inverse OperationsLike Addition is to SubtractionLike Multiplication is to Division52=25 and 25=582=64 and 64=8 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-20 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONS quare Numbers and Square Roots Square NumbersPos.

5 Square Roots12112242329342164522556236672497826 489281910210010 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-21 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONP erspectiveWhen taking a Square root , one question youcould ask yourself is:"What number times itself is the radicand? 36=?"What number times itself is 36?"PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-22/H-22 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONP ractice Taking the Square CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-23 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONA nswers to CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-24 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONQ uestionBetween which whole numbers is theSquare root of 45?

6 4545 is not a square number, but it isbetween two square < 45 < 49and36 < 45 < 49and 6 < 45 < 745 is a little less than ()PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsH-25 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONP racticeEstimate the value of67 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-25 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONP racticeEstimate the value of67 Since64 < 67 < 81and64 < 67 < 81and 8 < 67 < 967 is a little more than CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-26/H-26 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONC heck Your UnderstandingFill in the missing parts275 to the 4thpower(ab)(ab)(ab)121(a3b4) 538x8y88x3y54xy2(5)-2 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-27/H-27 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONC heck your UnderstandingPart 21.

7 Explain how 9 and 81 are related. 2. Without a calculator, identify the two integersbetween which the square root lies, and 30b. 72c. 12 PRIMARY CONTENT MODULE INUMBER SENSE: Exponents /Powers and RootsT-28 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATIONO pening ActivityYour rich uncle needs your help in his office for a 30day month. He made an unusual offer to pay you 1 the first day, 2 the second day, 4 the third day,each day doubling the previous days pay. Of course,you were insulted and were about to refuseemployment for the month when he said, "Ok, ok, Ireally need your help.

8 So how about $1, aday with $1, raise each day." You gladlyaccepted and your rich eccentric uncle laughed allthe way back to his office. What did you do thatwas so funny to him?