Laws of Exponents - California State University, …

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?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.

2 (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: 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.)

3 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: 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.

4 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?

5 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.

6 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. 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?