Textbook Practise DEEP PDF

DISCUSSION What difference, if any, is there between the operation of the index laws on numeric terms compared with similar operations on algebraic terms? Resources Resourceseses Interactivity Fourth Index Law (int-3716) Fifth and sixth index la...

DISCUSSION What difference, if any, is there between the operation of the index laws on numeric terms compared with similar operations on algebraic terms? Resources Resourceseses Interactivity Fourth Index Law (int-3716) Fifth and sixth index laws (int-6063) Exercise 2.3 Simplify algebraic products and quotients using index laws 2.3 Quick quiz 2.3 Exercise Individual pathways PRACTISE CONSOLIDATE MASTER 1, 3, 7, 9, 14, 15, 20 2, 5, 8, 10, 12, 16, 17, 21 4, 6, 11, 13, 18, 19, 22, 23 Fluency 1. WE9 Simplify each of the following. 3 10 4 12 )3 a. (e2 ) b. ( f 8 ) c. (p25 ) d. (r12 ) e. 2a2 ( 2. Simplify each of the following. 4 5 10 4 2 a. (a2 b3 ) b. (pq3 ) c. (g3 h2 ) d. (3w9 q2 ) e. (7e5 r2 q4 ) 3. Simplify each of the following. a. (p4 ) × (q3 ) WE10 b. (r5 ) × (w3 ) c. (b5 ) × (n3 ) d. (j6 ) × (g4 ) e. (2a) × (b2 ) 2 2 3 3 2 6 3 3 3 2 4. Simplify each of the following. a. (q2 ) × (r4 ) b. (h3 ) × (j2 ) c. ( f 4 ) × (a7 ) d. (t5 ) × (u4 ) e. (i3 ) × (j2 ) 2 5 8 8 4 3 2 2 5 6 5. WE11 Simplify each of the following. )2 ( 10 )2 )3 )2 3b4 5h 2k5 7p9 ( ( ( a. b. c. d. 3 d 2j2 3t8 8q22 6. Simplify each of the following. −4k2 −2g7 )3 )4 )3 )4 5y7 4a3 ( ( ( ( a. b. c. d. 3z13 7c5 7m6 3h11 Understanding 7. Simplify each of the following. a. (23 ) × (24 ) b. (t7 ) × (t3 ) c. (a4 ) × (a3 ) d. (e7 ) × (e5 ) 4 2 3 4 0 7 8 2 TOPIC 2 Indices and surds 71  8. Simplify each of the following. a. (g7 ) × (g9 ) b. (3a2 ) × (2a6 ) c. (2d7 ) × (3d2 ) d. (10r2 ) × (2r3 ) 3 2 2 3 3 4 2 (p7 ) ÷ p2 is equal to: 2 9. MC A. p7 B. p12 C. p16 D. p4.5 (w5 ) × (p7 ) 2 3 (w2 ) × (p3 ) 10. MC 2 5 is equal to: 6 A. w2 p6 B. (wp) C. w14 p36 D. w2 p2 (r6 ) ÷ (r4 ) is equal to: 3 2 11. MC A. r3 B. r4 C. r8 D. r10 12. Simplify each of the following. a. (a3 ) ÷ (a2 ) b. (m8 ) ÷ (m3 ) c. (n5 ) ÷ (n6 ) d. (b4 ) ÷ (b6 ) e. ( f 7 ) ÷ ( f 2 ) f. (g8 ) ÷ (g5 ) 4 3 2 4 3 2 5 2 3 2 2 2 a. (p9 ) ÷ (p6 ) b. (y4 ) ÷ (y7 ) 13. Simplify each of the following. 3 3 4 2 5 3 (c6 ) ( f 5) c. d. 2 4 (c5 ) ( f 2) 10 3 (k3 ) (p12 ) e. f. 8 2 (k2 ) (p10 ) Communicating, reasoning and problem solving 14. a. Replace the triangle with the correct index for the equation 47 × 47 × 47 × 47 × 47 = (47 ). ∆ c. If you rewrote the expression from part b without any exponents, in the format p × p × p..., determine 5 6 b. The expression (p ) means to write p5 as a factor how many times? how many factors you would need. d. Explain the Fourth Index Law. 15. a. Simplify each of the following. b. Write a general rule for the result obtained when −1 is raised to a positive power. Explain your answer. 10 7 15 6 i. (−1) ii. (−1) iii. (−1) iv. (−1) 16. Jo and Danni are having an algebra argument. Jo is sure that −x2 is equivalent to (−x) , but Danni thinks 2 otherwise. Explain who is correct and justify your answer. 3 17. A multiple-choice question requires a student to calculate (54 ). The student is having trouble deciding which of these three answers is correct: 564 , 512 or 57. a. Determine the correct answer. b. Explain your answer by using another example to illustrate the Fourth Index Law. 18. a. Without using your calculator, simplify each side of the following equations to the same base and then i. 8x = 32 solve each of them. ii. 27x = 243 iii. 1000x = 100 000 b. Explain why all 3 equations have the same solution. 72 Jacaranda Maths Quest 9 Stage 5 NSW Syllabus Third Edition