Simplify −6b 6 ÷ 2b 8 and give your answer with a positive index.
Answers
Answer:
1. (a) 1, 2, 7, 14 (b) 1, 3, 9, 27 (c) 1, 2, 3, 6 (d) 1, 3, 5, 15
(e) 1, 2, 3, 6, 9, 18 (f) 1, 5, 25 (g) 1, 2, 4, 5, 8, 10, 20, 40
(h) 1, 2, 4, 5, 10, 20, 25, 50, 100 (i) 1, 3, 5, 9, 15, 45
(j) 1, 2, 5, 10, 25, 50 (k) 1, 2, 3, 4, 6, 9, 12, 18, 36 (l) 1, 2, 4, 7, 14, 28
2. (a) 1 10 2 5 5 2 10 1 × ×× × ,,, (b) 1 82 44 28 1 ×× × × ,,,
(c) 1 77 1 × × , (d) 1 93 39 1 ××× , ,
(e) 1 16 2 8 4 4 8 2 16 1 × ××× × ,,,, (f) 1 22 2 11 11 2 22 1 ×× ×× ,,,
(g) 1 11 11 1 × × ,
(h) 1 24 2 12 3 8 4 6 6 4 8 3 12 2 × × ×××× × , ,,,,, , 24 1 ×
3. (a) 4 (b) 3 (c) 3 (d) 4 (e) 5 (f) 4 (g) 11
(h) 1
4. (a) 6, 10, 20, 8, 2, 24, 4 (b) 10, 20, 15, 55
5. (a) (i) 20, 22, 24, 26 (ii) 21, 24, 27 (iii) 20, 25
(b) prime numbers
6. (a) (i) 16 (ii) 18 (b) (i) 25 (ii) 27
1.5 Prime Factors
1. 2, 3, 5, 7, 13, 19, 23
2. 53, 59
3. (a) 2 5 × (b) 237 × × (c) 2 17 2 × (d) 2 37 3 × ×
(e) 2 53 × (f) 23 5 3 × × (g) 3 11 13 × × (h) 3 5 11 2 × ×
(i) 7 11 13 × ×
4. (a) 32 25 = and 56 2 7 3 = × (b) 2 8 3 (= )
5. (a) 236 × = (b) 236 × = (c) 3 5 15 × = (d) 2
(e) 2 5 10 × = (f) 5 7 35 × = (g) 2 3 24 3 × =
(h) 2 3 13 78 ×× = (i) 3 7 147 2 × =
6. (a) 45 3 5 2 = × , 99 3 11 2 = × , 135 3 5 3 = ×
(b) (i) 3 9 2 = (ii) 3 9 2 = (iii) 3 5 45 2 × = (c) 3 9 2 =
7. (a) 5 (b) 3 5 45 2 × = (c) 2 8 3 = (d) 2 5 10 × =
(e) 2 3 24 3 × = (f) 2 3 5 30 ××= (g) 2 3 108 2 3 × =
(h) 2 11 44 2 × = (i) 2 3 7
Step-by-step explanation:
1. (a) 1, 2, 7, 14 (b) 1, 3, 9, 27 (c) 1, 2, 3, 6 (d) 1, 3, 5, 15
(e) 1, 2, 3, 6, 9, 18 (f) 1, 5, 25 (g) 1, 2, 4, 5, 8, 10, 20, 40
(h) 1, 2, 4, 5, 10, 20, 25, 50, 100 (i) 1, 3, 5, 9, 15, 45
(j) 1, 2, 5, 10, 25, 50 (k) 1, 2, 3, 4, 6, 9, 12, 18, 36 (l) 1, 2, 4, 7, 14, 28
2. (a) 1 10 2 5 5 2 10 1 × ×× × ,,, (b) 1 82 44 28 1 ×× × × ,,,
(c) 1 77 1 × × , (d) 1 93 39 1 ××× , ,
(e) 1 16 2 8 4 4 8 2 16 1 × ××× × ,,,, (f) 1 22 2 11 11 2 22 1 ×× ×× ,,,
(g) 1 11 11 1 × × ,
(h) 1 24 2 12 3 8 4 6 6 4 8 3 12 2 × × ×××× × , ,,,,, , 24 1 ×
3. (a) 4 (b) 3 (c) 3 (d) 4 (e) 5 (f) 4 (g) 11
(h) 1
4. (a) 6, 10, 20, 8, 2, 24, 4 (b) 10, 20, 15, 55
5. (a) (i) 20, 22, 24, 26 (ii) 21, 24, 27 (iii) 20, 25
(b) prime numbers
6. (a) (i) 16 (ii) 18 (b) (i) 25 (ii) 27
1.5 Prime Factors
1. 2, 3, 5, 7, 13, 19, 23
2. 53, 59
3. (a) 2 5 × (b) 237 × × (c) 2 17 2 × (d) 2 37 3 × ×
(e) 2 53 × (f) 23 5 3 × × (g) 3 11 13 × × (h) 3 5 11 2 × ×
(i) 7 11 13 × ×
4. (a) 32 25 = and 56 2 7 3 = × (b) 2 8 3 (= )
5. (a) 236 × = (b) 236 × = (c) 3 5 15 × = (d) 2
(e) 2 5 10 × = (f) 5 7 35 × = (g) 2 3 24 3 × =
(h) 2 3 13 78 ×× = (i) 3 7 147 2 × =
6. (a) 45 3 5 2 = × , 99 3 11 2 = × , 135 3 5 3 = ×
(b) (i) 3 9 2 = (ii) 3 9 2 = (iii) 3 5 45 2 × = (c) 3 9 2 =
7. (a) 5 (b) 3 5 45 2 × = (c) 2 8 3 = (d) 2 5 10 × =
(e) 2 3 24 3 × = (f) 2 3 5 30 ××= (g) 2 3 108 2 3 × =
(h) 2 11 44 2 × = (i) 2 3 7
Answer: