1.9 Exercises 29
1.9 Exercises
Section 1.2
Calculate and express each result in its simplest form:
31 + 1 (−4) 2. 31 − 1 (−4) 3.(−3) − 1 (−4) 4.(−3) 1 × 1 (−4) 5. 31 × 1 (−4)
81 ÷ 1 (−4) 7.(−8) 1 ÷ 1 (−4) 8. 9. 10.
Section 1.3
Factorize in prime numbers:
- 6 23. 80 24. 256 25. 810
Simplify by factorization and cancellation:
Find the value of:
30.2! 32.7! 33.10!
Evaluate by cancellation:
Section 1.4
Express as decimal fractions:
- 10
− 2
- 21 × 110
− 3
- 21 + 131 × 110
− 4
1 + 151 × 110
− 6
Find the repeating sequence of digits in the nonterminating decimal fraction representation of:
Use the rules of rounding to give each of the following to 8, 7, 6, 5, 4, 3, 2 and 1 significant figures:
- 12131 = 1 0.07692 3076923 48. 49.π 1 = 1 3.141592 653589
Section 1.6
Simplify if possible:
50.a
2
a
3
51.a
3
a
− 3
52.a
3
a
− 4
53.a
3
2 a
2
54.a
5
2 a
− 4
55.(a
3
)
4
56.(a
2
)
− 3
57.(1 2 a
2
)
− 4
58.a
122
a
123
59.(a
2
)
322
60.(a
3
b
6
)
223
61.(a
3
1 + 1 b
3
)
123
- 9
122
- 8
223
- 32
325
- 27
− 423
Evaluate:
- 71 − 131 × 12 67. 71 − 1 (3 1 × 1 2) 68.(7 1 − 1 3) 1 × 12 69. 71 + 131 × 141 − 15
70.(7 1 + 1 3) 1 × 141 − 15 71. 41 ÷ 121 × 171 − 12 72. 41 ÷ 121 + 171 × 12 73. 81 × 121 ÷ 141 ÷ 12
- 31 + 14
2
- 31 + 141 × 15
2
- 251 + 1144
122
77.(5
2
1 + 112
2
)
122
2 1 414213562373=.
1
17
1
21
1
11
1
9
5
32
1
25
3
8
10
73
!
!!
5
32
!
!!
6
3
!
!
3
2
!
!
768
5120
63
294
21
49
3
18
1
3
1
9
÷
2
15
4
5
÷
2
3
5
3
÷
3
4
4
5
÷
−
×−
2
3
3
4
2
3
5
6
×
2
3
4
×
1
2
3
4
×
11
12
3
16
1
18
2
27
−
1
14
2
21
2
9
5
6
−
3
4
5
7
−
1
4
1
8