Grade 9 Exponents PDF

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and C...

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo. Play the Exponents less than and Greater than Game http://www.softschools.com/math/games/exponents_practice.jsp. You may also go to www.wiredmath.ca for the link. 1. Evaluate each power. 4 Recall some of the rules  3 a. 4 3 b.    5 c. − 7 6 d. (−4 ) 5 of exponents: 1. x 0 = 1, x ≠ 0 2. Write the following in exponential form. 2. x1 = x a. 11 × 11 × 11 × 11 × 11 b. 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 3. x m × x n = x m+ n 1 1 4. x m ÷ x n = x m− n , x ≠ 0 c. d. 2×2×2 7×7×7×7×7 5. (x m )n = x m× n e. 3 × y × y × y f. 2n × 2n × 2n × 2n × 2n 6. (xy) m = x m y m m 5 d ×d ×d ×6×6×6×6  x xm g. h. 7.  y  = y m , y ≠ 0 r×r×r×r 7×7× m× m× n (−5) × (−5y ) × (−5y) 2lk × 2lk × 3lk × 3l × 3k × 3k 1 i. j. 8. x −m = m , x ≠ 0 x 3. Write each as a repeated multiplication. 6  2 a. 9 5 b. 5s 4 c. (4a ) 2 d. −12 4 e.    n 3 4 2  1  2  116  f. 7 × −  g. −   h. 7 3 y 2 i. −53x 4 j.  3   2  3 m 4. Simplify. Leave your answer in exponential form. a. 7 3 × 7 2 b. 5 × 5 6 c. z 4 × z 8 d. 12 4 ÷ 12 3 e. 2 4 ÷ 2 4 f. p12 ÷ p 8 g. (32 )4 h. (2 4 )4 i. (s 3 )2 j. m11 ÷ m5 × m4 5. Write each expression as a simple positive power. 96 × 9 43 (−5)5 × (−5)3 (−6)8 a. b. c. d. 94 44 × 44 (−5)3 (−6)5 × (−6)5 6. Determine the value of x. a. 4 2 × 4 x = 4 6 b. 5 x × 5 3 = 5 9 c. t 3 × t x = t 4 d. 8 7 ÷ 8 x = 8 5 e. 7 x ÷ 7 9 = 7 f. m6 ÷ m x = m2 g. (4 2 )x = 4 8 h. (14 x )6 = 14 36 i. (b x )3 = b 3 j. 2 2 x × 23 = 2 Expectations: i) Substitute and evaluate algebraic expressions involving exponents ii) demonstrate understanding of exponent division, multiplication, and power 1 of a power. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.  Evaluate all of the powers of −3 up to (−3) , beginning with (−3)1. 10 7. a. i. When will (−3)n be negative? ii. Why do you think this is so? n b. i. When will (−3) be positive? ii. Why do you think this is so? 8. Simplify. Leave your answer in exponential form. a. 4 3 × 5 3 b. 10 8 × 38 c. 7 x × 8 x d. 5 2 × 5 2 × 5 2 + 5 6 e. 8 4 × 34 × 2 4 f. 9 t × 2 t × b t 9. Simplify. Leave your answer in exponential form. 43 67 10 v 10 9 62 a. b. c. d. e. 23 97 4v  1 9  52     2  2 10 24 5a 35 × 122 4a 2 × 2a 3 7 7 × 492 f. g. h. i. j.  22  2  25 a  217 16  21 4  4 2   125 a    3 10. a. On a quiz, Fauna wrote the following: 4 4 × 4 2 = 16 6. i. What mistake did Fauna make? ii. What does 4 4 × 4 2 equal? b. On the same quiz, Mark calculated 15 3 ÷ 5 2 = 31. i. What mistakes did Mark make? ii. Calculate 15 3 ÷ 5 2. 11. Lani’s giant rectangular backyard is 9 5 m long and 9 3 m wide. What is the area of the backyard? Express your answer in exponential form. 12. Keiko’s gigantic cube-shaped bedroom is 7 5 mm long. What is the volume of her bedroom? Express your answer in exponential form. CHALLENGE YOURSELF! 13. Simplify the following expressions: 4a x × 2a 6 1 1 5 2 a. b. 12 2 × 153 × 12 4 × 159 c. 215 × 47 × 8−22 16 3 5 7 1 − 94 × 96 xy 5 × y −34 x 9 7 4 × 7 −9 + 7 −5 d. e. f. ( )x −3 2 4 7 −12 (−y −18 ) x 6 y 5 7 14 11 − 93 × 95 2 18 Expectations: i) Substitute and evaluate algebraic expressions involving exponents ii) demonstrate understanding of exponent division, multiplication, and power 2 of a power. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.  EXTENSION 14. In the cross word below, solve for the value of α. (where there is an exponential solution, such as 25 , solve for the actual value). 1 2 3 4 – 5 6. 7. 8 9 10 11 12 – 13 14 Across Down 2. 59 ÷ 510 × α = 1 1. (5 + 2)3 = α −12c (6c3 )(−3c 2 ) 3 23 92 3 3. × 37 = α 2. =α (65 )6 6 6 (2 × 3c5 )2 4. 5d + 17c + 8d + α c = 13(d + c) 3. (−5pe ) ( pe) 3 2 −1 =α (2e)2 pe2 −3t 5 5. 23.5 × 2α × 43.6 = 2048 4. 2 = α3 24t 0.1(102 × 103 ) (0.12 ) (104 ) 2 3 3 6. =α 6. α 3 = 3581577n3 10 (10 ) (0.1 −3 3 7 4 × 0.1 )103 8. (−b−3 )5 = −bα 7. 3p × (951p − 183p) = α 2  7  7 2 2 (5u5c8 )( 9. 130   − 62   = α 10. −4u 2 cα ) = 20u 6 c 2+ 4o  2  2 −uc 6− o (o2 m12 × m15 ) (m8 × m3n4 )9 2 43 × 22n 164 11. = mα n y o z 11. = (m2 no0 )3 2α ÷ 83 2 −11u5s7 11u 2 12. = −729s (us3 ) α3 3 8x 25 y14 z 4 (3xyz ) 2 Did You Know? 13. =α 62 x 4 z 6 (x10 y 8 ) 2x 2 2 There are more than 272 possible grids of classic Sudoku. 89 (89α + 2 k ) × 89e l 59d 3 8915e kl 67 d × 892e+1 14. = l 4d +1 (8915e+3 k ) l 12d +1 × 8943e 2 Expectations: i) Substitute and evaluate algebraic expressions involving exponents ii) demonstrate understanding of exponent division, multiplication, and power 3 of a power. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.  The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo. Answers: 81 1. a. 64 b. c. −117 649 d. −1024 625 1 1 2. a. 115 b. 38 c. d. e. 3y 3 23 75 f. (2n )5 g. 5 h. d 3 64 i. (−5)3 y 2 j. 22 × 34 l 4 k 5 r4 7 2 m2 n 3. a. 9 × 9 × 9 × 9 × 9 b. 5 × s × s × s × s c. 4a × 4a d. −12 × 12 × 12 × 12  2  2  2  2  2  2  1  1  1 e.             f. 7  −   −   −   n  n  n  n  n  n  2  2  2  2  2  2  2 g. −         h. 7 y × 7 y × 7  3  3  3  3  116   116  i. −53× x × x × x × x j.    m × m × m  m × m × m 4. a. 7 5 b. 5 7 c. z12 d. 121 e. 2 0 = 1 f. p 4 g. 38 h. 216 i. s 6 j. m10 1 1 5. a. 9 3 b. c. (−5)5 d. 45 (−6 )2 6. a. 4 b. 6 c. 1 d. 2 e. 10 f. 4 g. 4 h. 6 i. 1 j. −1 7. −3, 9, −27, 81, −243, 729, −2187, 6561, −19683, 59049 a. i. (−3)n will be negative when n is odd. Rule: if a pair of numbers has the same sign, then their product is positive. Otherwise, their product is negative. ii. Since there will be an odd number of − ’s, the product will be negative. b. i. (−3)n will be positive when n is even. ii. Multiplying −3 by itself an even number of times will give a product that is positive. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca. 1  The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo. 8. a. 20 3 b. 30 8 c. 56 x d. 5 6 + 5 6 = 2 × 5 6 e. 48 4 f. (18b)t 7 v 3  2  5 9. a. 2 b.   c.   d. 20 9 e. 12 2  3  2 24 a5 f. 28 g. 5 2a h. i. j. 77 77 2 10. a. i. She multiplied bases with different exponents. ii. 4 6 = 4096 b. i. He divided bases with different exponents, and subtracted exponents with different bases. ii. 15 3 ÷ 5 2 = 5 × 33 = 135 11. 9 5 m × 9 3 m = 9 8 m 2 The area of the backyard is 9 8 m 2. (7 mm ) = 715 mm 3 The volume of Keiko’s bedroom is 715 mm 3. 5 3 12. 4a x × 2a 6 1 1 5 2 13. a. b. 12 2 × 153 × 12 4 × 159 c. 215 × 47 × 8−22 16 22 a x × 2a 6 1 5 + 1 2 + = 215+14−66 = = 12 2 4 × 15 3 9 24 7 5 = 2−37 3 x +6 = 2 a = 12 × 15 4 9 1 24 = x +6 237 a = 2 3 5 7 1 − 94 × 96 xy 5 × y −34 x 9 7 4 × 7 −9 + 7 −5 d. e. f. (− y ) (x )x −3 2 4 − 7 14 11 7 −12 9 ×9 2 3 5 −18 6 y 5 18 7 + 7 −5 −5 3 5 2 4 + − − = 7 −12 10 177 − =9 4 6 3 5 x9y 5 = 2 × 7 −5 7 37 − 222 = −12 =9 x9y 5 60 7 y9 = 2 × 77 = x −3 y 9 = x3 For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca. 2  The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo. 14. 1 2 3 5 3 4 6 4 – 4 5 6 0. 3 1 0 0 0 7 2 4 5. 8 9 10 11 12 – 1 5 8 3 3 2 5 9 13 14 e x p o n e n t s Down 1. (5 + 2) = α 3 2. −12c (6c3 )(−3c 2 ) 3 =α 3. (−5pe ) ( pe) 3 2 −1 =α 73 = α (2 × 3c5 )2 (2e)2 pe2 α = 343 2 3 × 35 × c10 52 p e 5 =α =α 22 × 32 × c10 2 2 p e4 2 × 33 = α 25 e=α α = 54 4 α = 6.25e −3t 5 4. 2 = α3 6. α 3 = 3581577n3 24t 1 1 1 − t3 = α 3 (α ) 3 3 = (3581577n ) 3 3 8 α = 153n 3  1   − t  = α 3 2 α = − 0.5t (5u5c8 )( 2 α ) 7. 3p(951p − 183p) = α 2 10. −4u c = 20u 6 c 2+ 4o −uc 6− o 2304 p 2 = α 2 20u5+ 2−1c8+ α −6+ o = 20u 6 c 2+ 4o (48 p) = α 2 2 c8+ α −6+ o = c 2+ 4o α = 48 p 8 + α − 6 + o = 2 + 4o α = 3o For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca. 3  The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo. 8x 25 y14 z 4 (3xyz ) 2 43 × 22n 164 −11u5s7 11u 2 11. = 12. = 3 13. =α 2α ÷ 83 −729s (us3 ) α 62 x 4 z 6 (x10 y 8 ) 2x 2 3 2 2 26 × 22n 216 5 7 11u 2 = 11u s = 23 × 32 x 27 y16 z 6 2α ÷ 29 2 =α 729u 3s10 α3 23 × 32 x 26 y16 z 6 26+ 2n− α +9 = 216−1 11u 2 11u 2 15 + 2n − α = 15 = 3 α=x 729s3 α α = 2n 11u 2 11u 2 = (9s )3 α 3 α = 9s 89 (89α + 2 k ) × 89e l 59d 3 8915e kl 67 d × 892e+1 14. = l 4d +1 (8915e+3 k ) l 12d +1 × 8943e 2 891+3α +6+ e−30e−6 k 3− 2 l 59d − 4d −1 = 8915e+ 2e+1− 43e kl 67 d −12d −1 891− 29e+3α kl 55d −1 = 891− 26e kl 55d −1 1 − 29e + 3α = 1 − 26e 3α = 3e α=e Across 23 92 3 2. 59 ÷ 510 × α = 1 3. × = α 4. 5d + 17c + 8d + α c = 13(d + c) 59−10 × α = 50 (6 ) 6 6 5 6 37 13d + (17 + α )c = 13d + 13c 5 ×α = 5 −1 0 23 × 34 = α 3 (17 + α )c = 13c 17 + α = 13 0 30+37 5 6 6 α = −1 3 × 5 6 3 = α 3 α = −4 α =5 6 67 6 3 3 64 = α 6 6 α = 64 0.1(102 × 103 ) (0.12 ) (104 ) 2 3 3 5. 2 × 2 × 4 3.5 α = 2048 3.6 6. =α 8. (−b−3 )5 = −bα 10−3 (103 ) (0.14 × 0.13 )10 7 23.5 × 2α × 27.2 = 211 −b−15 = −bα 23.5+ α +7.2 = 211 0.17 × 1022 α = −15 =α 10.7 + α = 11 0.17 × 1019 α = 0.3 103 = α α = 1000 For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca. 4  The CENTRE for EDUCATION in MATHEMATICS and COMPUTING NUMBER SENSE AND NUMERATION: EXPONENTS This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo.  7 2  7 2 (o2 m12 × m15 )9 (m8 × m3n4 )2 9. 130   − 62   = α 11. = mα n y o z  2  2 (m2 no0 )3  49    × 68 = α o18 m265 n8 = mα n y o z 4 mno6 3 0 49 × 17 = α m259 n5o18 = mα n y o z α = 833 α = 259 For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca. 5