1. ก F 1
กก
กก
F a n ก
an F F กก ก
กก an กa F ก n F ก
F F
2 × 2 × 2 × 2 × 2 = 25
5 × 5 × 5 × 5 × 5 × 5 = 56
12 × 12 × 12 × 12 = 12 4
ก F F กF กก
ก F F F ก 25 , 56 12 4 F กก
ก 25 F F กก F ก F
ก2 F
ก5 F ก
ก F ก
F 1
กก ก FF
(1) 23 ก
2× 2× 2 = 8
(2) (− 3) 4
ก ก F
(− 3) × (− 3) × (− 3) × (− 3) = 81
(3) (− 4)5 ก F ก
(− 4) × (− 4) × (− 4) × (− 4) × (− 4) = −1024
ก F F กก ก F F F
ก FF ก F F
ก F F F F 1–3

2. F 2
F กก
(1) 8
8 = 2 × 2 × 2 = 23
(2) 27
27 = 3 × 3 × 3 = 33
(3) 32
32 = 2 × 2 × 2 × 2 × 2 = 2 5
F 3
ก ก ก F ก F F Fก
F F 36 63
3 6 = 3 × 3 × 3 × 3 × 3 × 3 = 729
6 3 = 6 × 6 × 6 = 216
F ก ก F F Fก

3. ก F 2
1 กก
1
F a m n ก F
a m × a n = a m+n
ก F ก
F 1
F F กก F 1
(1) 10 4 × 10 5
10 4 × 10 5 = 10 4+ 5
= 10 9
10 9
(2) 38 × 3 5
38 × 3 5 = 38 + 5
= 313
313
(3) (− 5)3 × (− 5)4
(− 5)3 × (− 5)4 = (− 5)3+ 4
= (− 5)
7
(− 5)7
(4) (− 2)12 × (− 2)5
(− 2)12 × (− 2)5 = (− 2)12+5
= (− 2 )
17
(− 2)17
ก F กก ก F ก กก
ก F 1-4

4. ก F 3
2 กก
2
F a m n F
(a )
m n
= a m×n
ก F ก
F 1
F F กก F 2
(1) (9 ) 2 5
(9 ) 2 5
= 9 2×5
= 910
910
(2) (4 )
3 −4
(4 ) 3 −4
= 4 3×(−4 )
= 4 −12
4 −12
(3) (3 )
−6 3
(3 ) −6 3
= 3 (−6 )×3
= 3 −18
3−18
(4) (15 ) − 4 −7
(15 ) − 4 −7
= 15 (−4 )×( −7 )
= 15 28
15 28
ก F กก ก F ก F F ก ก

5. ก F 4
3 กก
3
F a b m ก F
(a × b )m = am × bm
ก F ก
F 1
F F กก F 3
(1) (7 × 5)2
(7 × 5)2 = 7 2 × 5 2
7 2 × 52
(2) (7 × 5)2
(7 × 5)2 = 7 2 × 5 2
7 2 × 52
(3) (7 × 5)2
(7 × 5)2 = 7 2 × 5 2
7 2 × 52
(4) (7 × 5)2
(7 × 5)2 = 7 2 × 5 2
7 2 × 52
ก F ก F ก F ก
F ก F F ก F 1-4

6. ก F 5
4 กก
4
F a b b≠0 m ก F
m
a am
FF   = m
b b
ก F ก
F 1
F F กก F 4
2
 3
(1)  
9
2
 3 32
  = 2
9 9
32
92
6
5
(2)  
3
6
5 56
  = 6
3 3
56
36
8
−9
(3)  
 11 
−9 (− 9)
8 8
  =
 11  118
(− 9)8
118
7
 15 
(4)  
 − 20 
7
 15  15 7
  =
 − 20  (− 20)7
15 7
(− 20)7
ก F ก F ก F ก F
ก F F ก F 1-4

7. ก F 6
5 กก
5
F a a≠0 ,m n ก F
am
FF n
= a m−n
a
ก F ก
F 1
F F กก F 5
35
(1)
32
35
2
= 35− 2
3
= 33
33
89
(2)
87
89
= 8 9 −7
87
= 82
82
911
(3)
915
911
15
= 911−15
9
= 9 −4
9 −4
48
(4)
4 20
48
= 4 8−20
4 20
= 4 −12
4 −12
ก F กก ก F ก F ก ก
F ก F 1-4

8. ก F 7
1
a0
an
F a a≠0 F a0 = 1
1
F a a≠0 n F n
= a −n
a
ก F ก
F 1
F F กก F 5
(1) 50
50 = 1
1
(2) 12 0
12 0 = 1
1
1
(3)
95
1
= 9 −5
95
9 −5
1
(4)
42
1
= 4 −2
42
4 −2
ก F 1. กก ก F F Fก
2. F F กก ก
ก F Fก กก ก
F ก F 1-4

9. ก F 8
ก F กก ก ก
ก F ก
F F กก ก ก
58
(1)
510
58
10
= 5 8−10
5
= 5 −2
1
= 2
5
1
52
10
(2)
10 2
10
2
= 101− 2
10
= 10 −1
1
=
10
1
10
 1 
(3)  3 ÷4
2
4 
 1  −3
 3 ÷4 = 4 ÷4
2 2
4 
= 4 −3 − 2
= 4 −5
1
= 5
4
1
45
− 72
(4)
− 74
− 72
= (− 7 )
2−4
−7 4
= (− 7 )
−2
1
=
− 72
1
− 72

10. ก F 9
ก กก F ก กก F F F F
ก F ก
F 1
F F กก F F
 55 
(1) 52 ×  3 
5 
 
 55 
5 × 3 
2
5  = 5 2 × (5 5−3 )
 
= 52 × 52
= 5 2+ 2
= 54
54
 75 
(2) (7 4
× 72 ÷  2
7 ) 

 
 75 
(
7 ×7 ÷ 2
4
7
2
)  = (7 4+ 2 ) ÷ (7 5− 2 )

 
= 76 ÷ 73
= 7 6 −3
= 73
73
(3) (9 ) × (9
6 3 2
×9 )
(9 ) × (9
6 3 2
)
× 9 = 918 × 9 2+1 ( )
= 918 × 9 3
= 918+3
= 9 21
9 21
4
 43 
(4)  2
5 
 
4
 43  4 3×4
 2  = 2×4
5 
  5
412
= 8
5
12
4
58

11. ก F 10
กก 10
F ก ก F กก 10 , 100 , 1,000 , 10,000 ,
100,000 , 1,000,000
F F กก 10 F
10 = 101
100 = 10 × 10 = 10 2
1,000 = 10 × 10 × 10 = 10 3
10,000 = 10 × 10 × 10 × 10 = 10 4
ก FF ก F ก F F
100,000 F F6 ก ก Fก 6
100,000 = 10 6
ก ก F F กก F F
ก F
F 2 7,200,000 ก
7,200,000 = (7 × 1,000,000) + (2 × 100,000)
(
= 7 × 10 6 + 2 × 10 5) ( )
F 2 578,000 ก
578,000 = (5 × 100,000) + (7 × 10,000) + (8 × 1,000 )
( ) (
= 5 × 10 5 + 7 × 10 4 + 8 × 10 3 ) ( )
F 3 23,459 ก
23,459 = (2 × 10,000) + (3 × 1,000) + (4 × 100 ) + (5 × 10) + (9 × 1)

12. ก F 11
ก F F
ก F F ก ก 10 ก
F1 F F 10
ก F F F a × 10 n 1 ≤ a < 10
n ก 1 ≤ a < 10 F a F F F F 10
ก F ก ก F F
F F F ก F F ก F ก ก
10 F F
F ก
F ก F F
1.) 5,400,000
5,400,000 = 54 × 10 × 10 × 10 × 10 × 10 = 54 × 10 5
= 5.4 × 10 × 10 × 10 × 10 × 10 × 10 = 5.4 × 10 6
5,400,000 = 5.4 × 10 6
2.) 659,000,000
659,000,000 = 659 × 10 × 10 × 10 × 10 × 10 × 10 = 659 × 10 6
= 65.9 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 65.9 × 10 7
= 6.59 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 6.59 × 10 8
659,000,000 = 6.59 × 10 8
3.) 32,054,100
32,054,100 = 320,541 × 10 × 10 = 320,541 × 10 2
= 32,054.1 × 10 × 10 × 10 = 32,054.1 × 10 3
= 3,205.41 × 10 × 10 × 10 × 10 = 3,205.541 × 10 4
= 320.541 × 10 × 10 × 10 × 10 × 10 = 320.541 × 10 5
= 32.0541 × 10 × 10 × 10 × 10 × 10 × 10 = 32.0541 × 10 6
= 3.20541 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 3.20541 × 10 7
32,054,100 = 3.20514 × 10 7
4.) 10,000,000
10,000,000 = 1 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1 × 10 7
10,000,000 = 1× 10 7

13. F F ก F F
F ก F F9 F ก F F
F 10 9 ก F F F
ก F F
1,564,000
1 5 6 4 0 0 0
F 1 F 2 F 3 F 4 F 5 F 6
1,564,000 F6 F ก F F 1,564,000 = 1.5 × 10 6

14. ก F 12
ก F F ก F F
F ก 0.0000000005 ก F FF ก ก ก F
F a × 10 n 1 ≤ a < 10 n F a F F
F F 10
F ก
F F F ก F F
1.) 0.5
0.5 = 5 × 10 −1
0.5 = 5 × 10 −1
2.) 0.06
0.06 = 6 × 10 −2
0.06 = 6 × 10 −2
3.) 0.007
0.007 = 7 × 10 −3
0.007 = 7 × 10 −3
4.) 0.00326
0.00326 = 3.26 × 10 −3
10,000,000 = 1× 10 7
5.) 0.00000004567
0.00000004567 = 4.567 × 10 −8
F F ก F F ก FF ก
F F 15 ก F F 10 −15 F F
F F ก
F 10 −15 F F F1 F F 10 ก F F F
ก F Fก ก
ก 10 F
0.0000123 = 000001.23 × 10 −5 ก F 5 F
0.0000123 = 1.23 × 10 −5

15. ก F 13
ก ก F ก F F
ก ก ก F F ก F Fก
F ก F F ก กF F
F ก
F F F ก F F
1.) (5 × 10 ) + (6 × 10 )
7 5
ก F F ก กF 10 7 F 10 5
(5 × 10 ) + (6 × 10 ) = (500 × 10 ) + (6 × 10 )
7 5 5 5
= (500 + 6 ) × 10 5
= 506 × 10 5
= 5.06 × 10 7
(5 × 10 ) + (6 × 10 ) = 5.06 × 10
7 5 7
2.) (9 × 10 8 ) + (11 × 10 9 )
ก F F ก กF 10 9 F 10 8
(9 × 10 ) + (11 × 10 ) = (9 × 10 ) + (110 × 10 )
8 9 8 8
= (9 + 110 ) × 10 8
= 119 × 10 8
= 1.19 × 1010
(9 × 10 ) + (11 × 10 ) = 1.19 × 10
8 9 10
3.) (6 × 10 7 ) − (5 × 10 4 )
ก F F ก กF 10 7 F 10 4
(6 × 10 ) − (5 × 10 )
7 4
= (6000 × 10 4 ) − (5 × 10 4 )
= (6000 − 5) × 10 4
= 5995 × 10 4
= 5.995 × 10 7
(6 × 10 ) − (5 × 10 )
7 4
= 5.995 × 10 7

16. 4.) (5 × 10 4 ) + (6 × 10 6 ) − (3 × 10 5 )
ก F F ก กF 10 6 10 5 F 10 4
(5 × 10 ) + (6 × 10 ) − (3 × 10 ) = (5 × 10 ) + (600 × 10 ) − (30 × 10 )
4 6 5 4 4 4
= (5 + 600 − 30 ) × 10 4
= 575 × 10 4
= 5.75 × 10 6
(5 × 10 ) + (6 × 10 ) − (3 × 10 ) = 5.75 × 10
4 6 5 6
5.) (21 × 10 8 ) − (8 × 10 6 ) + (25 × 1010 )
ก F F ก กF 1010 10 8 F 10 6
(21× 10 ) − (8 × 10 ) + (25 × 10 ) = (2100 × 10 ) − (8 × 10 ) + (250000 × 10 )
8 6 10 6 6 6
= (2100 − 8 + 250000 ) × 10 6
= 252092 × 10 6
= 2.5292 × 1011
(21× 10 ) − (8 × 10 ) + (25 × 10 ) = 2.5292 × 10
8 6 10 11

17. ก F 14
ก F ก F F
F ก
F F F ก F F
1.) (5 × 10 )× (6 × 10 )
7 5
(5 × 10 )× (6 × 10 ) = 5 × 6 × 10
7 5 7
× 10 5
= 30 × 10 7 + 5
= 30 × 1012
= 3 × 1013
(5 × 10 )× (6 × 10 ) = 3 × 10
7 5 13
2.) (9 × 10 8 )× (11 × 10 9 )
(9 × 10 )× (11 × 10 ) = 9 × 11× 10
8 9 8
× 10 9
= 119 × 10 8+ 9
= 119 × 1017
= 1.19 × 1019
(9 × 10 )× (11 × 10 ) = 1.19 × 10
8 9 19
3.) (6 × 10 7 ) ÷ (2 × 10 4 )
6 × 10 7
(6 × 10 ) ÷ (2 × 10 )
7 4
=
2 × 10 4
= 3 × 10 7 − 4
= 3 × 10 3
(6 × 10 ) ÷ (2 × 10 )
7 4
= 3 × 10 3
4.) (55 × 10 8 ) ÷ (5 × 10 6 )
55 × 10 8
(55 × 10 ) ÷ (5 × 10 )
8 6
=
5 × 10 6
= 11 × 10 8−6
= 11× 10 2
= 1.1 × 10 3
(55 × 10 ) ÷ (5 × 10 ) = 1.1 × 10
8 6 3

18. 5.) (7 × 10 8 )× (3 × 10 6 ) ÷ (3 × 1010 )
(7 × 10 )× (3 × 10 ) ÷ (3 × 10 ) = (7 × 10 ×)10(3 × 10 )
× 8 6
8 6 10
10
3
7 × 3 × 10 8 × 10 6
=
3 × 1010
21 × 10 8+ 6
=
3 × 1010
7 × 1014
=
1010
= 7 × 1014−10
= 7 × 10 4
(7 × 10 )× (3 × 10 ) ÷ (3 × 10 ) = 7 × 10
8 6 10 4
6.) (162 × 10 21 ) ÷ (29 × 10 8 )× (3 × 1011 )
(162 × 10 ) ÷ (29 × 10 )× (3 × 10 ) = (29 ×(162 )××10 ×)10 )
21
21 8 11
10 (3 8 11
162 × 10 21
=
29 × 3 × 10 8 × 1011
162 × 10 21
=
81 × 10 8+11
162 × 10 21
=
81 × 1019
= 2 × 10 21−19
= 2 × 10 2
(162 × 10 ) ÷ (29 × 10 )× (3 × 10 ) = 2 × 10
21 8 11 2