เลขยกกำลัง

เอกสารประกอบการเรียนการสอน 5

คณิตศาสตรพ์ ้นื ฐาน ค 32101 เทอม 1

บทท่ี 1

เลขยกกาลงั

MATH ครูผู้สอน

นายพรชัย ศริ ริ ัตน์
นางสาวันซัลมา ปานากาเซง็
นางสาวนูรฮานัน คามสิ
***กลุ่มสาระการเรยี นรู้คณิตศาสตร*์ **

EXPONENT
โรงเรยี น คณะราษฎรบารุง จงั หวดั ยะลา

1

1.1

a n
an a a a ... a
an
n
a
n

PROBLEMS

1.

1) 26 222222 64
2) ( 4)3
3) 1 5 _____________________ ___

5 _____________________ ___
4) (0.03)3 ___
5) (x y)5 _____________________
_____________________

2.

1) 7 7 7 __________
__________
2) (0.2) (0.2) (0.2) (0.2) __________

3) ( 4) ( 4) __________

4) 1 1 1 11 __________
2 2 2 22 __________
4 4 __________
5) 4 5 5
5 bb bbb

6) a a a

7) (a a b b c c)

3 32101 1

a, b m, n

1) an am an m
2) am
am n
an
3) (am )n a mn
4) (ab)n a nb n
5) a n
an ,b 0
b bn
6) a 0
1 ,a 0
7) a n
1 ,a 0
an

1 m, n

a, b am an am n

1. 37 33 __________________________
2. ( 343) 78 __________________________
3. 125 52 __________________________
4. ( 2)4 23 __________________________
5. ( 3)2 33 ( 3)4 ___________________________
6. 8 23 ( 2)3 ___________________________
7. x 3 ( x)4 x 5 ___________________________

2 m, n
am an am n
a, b
___________________________
1. 27 23 ___________________________
2. (42 43 ) 44 ___________________________
3. (m2 m 3 ) m 4 ___________________________
4. (a2 a) (a 3 a5 ) ___________________________
5. a 4 a2 a 3

a 7 a 8 a12

3 m, n a mn
(am )n
a, b
___________________________
1. (23 )5 ___________________________
2. (( 2)3 )4 ___________________________
3. ((xy)5 )52 ___________________________
4. (x n )2n 1 ___________________________
5. (yn 1 )n 1
m, n
4 (a b)n

a, b

an bn

1. (2 3)4 ___________________________
2. (( 2)4 327 )3 ___________________________
3. (abc)n ___________________________
4. ((xy)ab )ab ___________________________
5. ((a 3b 4 )3a )a4 ___________________________
6. [(a 3b2c 1)3 (a2b3c 2 )]2 ___________________________

5 m, n

a, b an
b
an
bn

1. 2 3 ___________________________
5 ___________________________
___________________________
2. ( 5)8 3 ___________________________
6252

3. 33 83 2

27 64

4. ab3c 1 2
a 2b 1c

3 32101 1

6

a, b m, n
a 0 1, a 0

1. 30 20200 _______________________
2. ( 2345)0 _______________________
_______________________
3. ( 3)0 _______________________
4. ( 1)20 ( 1)04 _______________________
5. (020 )0 _______________________
6. (32 25 )0 _______________________
7. 10 20 30 ...

7

a, b m, n
a n 1 ,a 0
an

1) a 0 a0

2) a n n a0

1

3) a a0 n an

a0 00 indeterminate form ( )

1. 2 3 _______________________
2. 5 2 6 3
3. 1 _______________________

24 _______________________
4. a 1b 2c 3
_______________________
d 1e 2 f 3
5. x 2y 3 1 _______________________

abc _______________________
6. a 1 b 2 a 1

b ab

PROBLEMS

1. 86 45
2. 25 23

24
3. 63 32

24 3 2

4. 6 3 105
5

23 3 4 3 2 3 32 5
22 3 2 31
5.

21 22 23 ... 2 2020 2
6. .... 22020

21 22 23

3 32101 1

PRACTICE 1.1.1

1. 3 2 158 0

2. 23 4 2 32 2 8 1

3. 22 103
54 25

4. 2 3 3 5
3 5 20

3 1 3 2 3 3 3 4 ... 3 2020 9
5.

3 1 3 2 3 3 3 4 ... 3 2020

PROBLEMS z

a,b, n, x, y

1. a 1
a b1

2. x 3 y2x
yz

3. x4 2

2y 2 2xy2 3

4. x 5y7 x 2y 7z 0

5. 3102 3100 50
3100 5

3 32101 1

a,b, n, x, y z PRACTICE 1.1.2

1. (a b) 1
a1 b1

2. x 3y 2 x 5y3

3. y4 1 y2 12y 8
3

4. 3 2n 1 4 2n 2
2n 2n 1

5. 1 x 3y2 4
2

x 2y3 xy4 3
6.

x 2y

a m, n

a 1( ) mn am an
0 a 1(
) mn am an

PROBLEMS 3217 649

1.

2. 31253 2517 ___________
___________
3. 268 351 ___________

4. (0.5)27 (0.25)13 ___________
___________
5. (0.1)46 (0.01)69 ___________

6. 2 124 4 62

PROBLEMS

1. a 325, b 520, c 715, d 910

_________________

3 32101 1

2. a 245, b 336, c 427 , d 518, e 69

3. a 2 9, b 5 6, c 3 6, d 7 6 _________________
_________________

PRACTICE 1.1.3

1.
1) (0.1)39, (0.23)26, (0.75)13

_________________

2) 732 , 497, 723

_________________

3) 4911, 3433, 24012

_________________

4) 2100, 3600, 10300

_________________

1.2 n

ab a b2 a
b

4 16 42 16
12 1
1 1 39
3 9
( 5)2 5
5 5
a a
a a

PROBLEMS 25 25 5 5

1. 81 81 9 9
1)
2) 5 55 5
3)
4) 16 ___________________________
5) 144 ___________________________
6) 400 ___________________________
16 ___________________________
2. x 2 16 63 ___________________________
0.64 ___________________________
x

3. y 2 15 7 81 3 25 5 y

16 80 24

3 32101 1

a0 b0

1) a a a

2) ( a )2 a

3) a2 a

4) a b ab

5) a a ,b 0
b b

7 6 7 6 42

14 14 7
2
2 _____________________________
_____________________________
PROBLEMS _____________________________

4.

1) 50

2) 625

3) 72 2

4) 3 12 _____________________________
8 _____________________________

5) 132

6) 12 2 _____________________________
13

7) 63 112 _____________________________
7 175

n

n 1a b
b a bn a

2 3 na

n

n n a0 n n a0
1. n a na 1. n a na

a0 a
2. a 0 2. a 0
3. a 0 3. a 0

2

4. a 0 n 4. a 0 na

a 4 16 24 16

2 4 16 ( 2)4 16
2
3 5 243 ( 3)5 243

4 16 2 2
3
5 243

PROBLEMS

5.

1) 3 343 _________________________
_________________________
2) 3 1 2 5 _________________________
_________________________
3) 4 1 6 _________________________
_________________________
4) 4 256 _________________________

5) 5 3 2

6) 5 2 3

7) 6 1

a 0 n 1 a
1. a n a
n
na na

2. a n n
na
na

3 32101 1

a nb n
a
1. b n a
2. ab 0

1. 4 625 4 625 5
2. 6 729 6 729 3
3. 9 512 9 512
4. 5 1, 024 2
5 1, 024
4

1. n “ ” n “”

“ ” 3 3
2
2. n2 na
a na
3. a n
39 39
1. 3 9 4 15 4 15
2. 4 15 5 50 5 50
3. 5 50

PRACTICE 1.2.1

1. 2 2a

1) a 121 2) a 169 3) a 576

____________ ____________ ____________

4) a 72 5) a 243 6) a 1, 728

____________ ____________ ____________

2. 3 3

1) a 343 2) a 216 3) a 512

____________ ____________ ____________

4) a 1, 029 5) a 1, 080 6) a 1, 024

____________ ____________ ____________

n

ab n
1. (n a )n a

2. n a n b n ab

3. n a a ,b 0
nb
n

b

PROBLEMS

6.

1) 3 4 3 2 _______________________________
_______________________________
2) 3 4 3 16 _______________________________
_______________________________
3) 3 8 ( 27) _______________________________

4) 4 16 81 _______________________________

5) 4 324 _______________________________
44

6) 3 27
64

7) 81 16
25

a n n2
n
1. n an a n
2. n an a

PROBLEMS ________________________________
________________________________
7. ________________________________
1) 32 ________________________________
2) ( 3)2
3) 3 53 6 x 6 ____________________
4) 3 ( 5)3
5) x

3 32101 1

8. a b 2) 4 81a 8 b12

1) a 6 b 4

9. a 0 b0
1) a 2b 8
2) 3 a 6b 9

x m nx mn

a na m
m na
m2
m n a mn a

PROBLEMS ________________________________

10.

1) 16

2) 3 a 6 ________________________________

3) a3 3 18 ________________________________

4) a5 3 30 ________________________________

11. a b 4 256a 8b24

a na na m
na
m2 m a0
1. mn am m
2. mn am

PROBLEMS ________________________________

12.

1) 8 24

2) 9 ( 4)3 ________________________________

3) 15 125 ________________________________

4) 12 256 ________________________________

13. a 0 b 0 24 a 12b16 a 3 b2

14. 12x 3y5z 2 x, y, z

15. x y 3 6x 2y 3 4x 5y2 2x 2y 3 3x

3 32101 1

PRACTICE 1.2.2

1.

1) 36 25 2) 3 125 27 3) 4 256 81
____________ ____________ ____________
____________ ____________ ____________
____________ ____________ ____________

4) 3 64 5) 196 6) 5 243
125 625 1, 024

____________ ____________ ____________
____________ ____________
____________ ____________ ____________

____________

2. x, y z

1) x 10y 4z 2 2) 3 x 12y15z 18 3) ( 2)2 x 2y 4

____________ ____________ ____________

____________ ____________ ____________

____________ ____________ ____________

3. x, y z

1) 3 125x 6y9z 3 2) x 6y 8 3) 16x 4z 16
____________ z4
____________ 4
____________ ____________ y 20
____________
____________ ____________

____________

____________

4. a, b

1) 3 64 2) 5 1, 024 3) 3 5 ( 1)7
____________ ____________ ____________
____________ ____________ ____________
____________ ____________ ____________

4) 3 a12 5) a 8b12 6) 4 a 24b8
____________ ____________ ____________
____________ ____________ ____________
____________ ____________ ____________

PROBLEMS 52

16.
1) 4 2

2) 2 2 5 2 4 2

3) 63 112 175

4) 3 5 2
3

5) 3 8 3 216 3 343

6) 2 a 4x 3a 2 4x 9a 4x

17.
1) 3 2 3 3
2) 3 2 4 3 5
3) 2( 3 5)
4) 2 3( 2 5)

3 32101 1

5) (4 7)(3 2)

6) (3 5 7 2)( 5 3 2)

PRACTICE 1.2.3

1.
1) 3 3 34 3 4 3
2) 45 3 20 4 5

3) 4 81 8 3 216 15 2 32 225

4) 3 45 125 200 50

5) 72 800 18

2.
1) 3 5( 10 2 5)
2) (3 3)2
3) (4 7)(3 2)

PROBLEMS

18.
1) 32
5

2) 13 17
6

3) 3
51

4) 1
22 3

5) 3 2
3 2

6) 4 54 5
4 54 5

3 32101 1

(a b) 2 ab ( a b)

(a b) 2 ab ( a b) ab

PROBLEMS

19.

1) 14 2 45

2) 13 2 42

3) 10 2 24
4) 18 8 5

5) 11 2 30

6) 7 48 12 2 27
7) 12 6 3 3

PRACTICE 1.2.4

1.
1) 2

33

2) 40
3

3) 1
65

4) 3 2
3 2

5) 5 2 3
7 43

2.

1) 5 2 6

2) 13 112

3) 12 6 3

3 32101 1

1.3

1 1
nn 1

a n
an
1

an n a

a0 1

an

a0 n

1

82 8 4 2 4 2 2 2

1 4

( 64)3 3 64 3 64 3 43

PROBLEMS

1.

1 1

1) 164 2) ( 81)4

____________ ____________

1 1

3) ( 125)3 4) (( 11)2 )4

____________ ____________

1 1

5) (( 25)2 )6 6) (( 49)2 )6

____________ ____________

1 a, b R 1 a, b R

7) (ab)4 8) (a b)8

____________ ____________

a a0 rp p, q
q
q0
1

. . . p, q 1 aq

p 1p

ar aq aq

1)

1

aq

14 7

( 8) 6 ( 8)3 (3 8)7 ( 2)7 27 128

1 1

( 9)2 ( 9)2

2) a0 r 0r 0

0r r

PROBLEMS 7

2. 2) ( 81)14

4 ____________

1) 258 1

____________ 4) (( 27)10 )6

1 ____________

3) (1252 )4 1

____________ 6) (( 64)4 )2

1 ____________

5) ((64)4 ) 2 1

____________ 8) (04 ) 2

2 ____________

7) 03

____________

mn ab 0
am, an
bn

1) am an am n

2) am am n
an

3) (ab)n an bn

4) a n an
b bn

5) (am )n a mn

3 32101 1

PROBLEMS a, b 0

3.

1) 3

1002

2) 5

81 4

3) 2

3 36

4) 2 11

363 36 6

3 4

5) 1, 0002 9

2

6) 243
2
33

4.

1

1) (27a3)6

1

2) (8ab 2 )3

1

(16a 2b 2 )4

3) 33 5 4 3 40 2

3203
6 1, 600

2

4) a 3 b 2 b2 a 2
b2 a 2 4

a3

2 1

5) ( a ) 3 b4 ab 2 a 2b 3

6) 4 81 8 1024 8 324
48 49

3 32101 1

PRACTICE 1.3.1

1. 1 1 1

1 4(40)3 (1600)6 10 8 3
25
1) 3(5)3

2) 5 3 4 2 3 32 3 108

3) 3 81 3 375 3 192

3 xy y
x3 yx
4) y 2
xy

11

5) 82 ( 8)3

11

82 ( 8)3

o-net

2

1. 83 2 (0-net 65)

125 32

2. x,y, z x 2y4z2 xy2z
(0-net 65)

3. a b 1 6a
(0-net 64)
1 1
1
2. a b6 3. a b3
1. a b12 5. a b12

4. a b3

4. 6 2 (0-net 63)
3
48
3 33 16 23 54

3 32101 1

5. (0-net 64) 4. ) )
) 10010 10100 5. ) )

)2

4 5 5 24

) 3 14 4

27 13

27

)) )

1. )

2. )

3. )

6. x 1 12 24 (0-net 64)

34 24

1. 0 x 1

4

2. 1 x 1

42

3. 1 x 1
2
4. 1 x 2

5. 2 x 4

7. a (0-net 63)
1. 2 a 2
24

2. a2 9 a2 3

3. 2 a2 1 2a2 2

4. a 2 2 a2 4

5. 2a 4 3 8 a 2 3

8. 3 1 3 (0-net 63)

3 31

9. ( 4 (0-net 63)

5)5

1. 5 54

2. 4 55

3. 4 55

4

4. 1 5
5

5

5. 1 4

5

3 32101 1

1.4

PROBLEMS 3%
1. 10, 000
1
1)

2) 2

() p i% ri
p(1 r)n 100
n
5
2. 0.5%
1)
30, 000

2) 9 100, 000

3. 100, 000 10
10 110, 462.21

4. 15, 000
1) 5

22
35

2) 70, 000

3 32101 1

1. 1 1.2 o-net 5
(o-net 65)
2,500
4

2. 10, 000

15, 000

3 (o-net 65)

3. 2,00,000

(0-net 65)

() 1234
(
) 1, 880, 000 1, 760, 000 1, 640, 000 1, 520, 000

4. 3
63
6%
11,940.52
3
(0-net 64)

5. 1 500 2%
1 2564
31 1
1. 500 (0-net 64)
2. 500 2574
3. 500 500(1.02)2 500(1.02)10
4. 500 500(1.02)
5. 500 500(1.02) 500(1.02)2 500(1.02)11
500(1.02)
500(1.02) 500(1.02)2 500(1.02)3 500(1.02)10
500(1.02)
500(1.02)2 500(1.02)3 500(1.02)11

500(1.02)2 500(1.02)3 500(1.02)12

3 32101 1

6. 7,000 “ 31 2571
0.2 ” 31 2583
2583 31
1. 7, 000(0.2)12 (0-net 64)
2. 7, 000(1 0.2)12
3. 7, 000(1 0.002)12
4. 7, 000(1 0.2)13
5. 7, 000(1 0.002)13

7. 30,000 3%
4
8
(0-net 64)

PRACTICE 1.4.1

1. 1%

10, 000 10
20, 000
5

2. n i n n0(1 r)i n0

2559 r ..
1.13%
. . 2559 7.4

3. 20,000 5
5 22,081.62

3 32101 18,000 1
24
4. 80,000
7
50,000
1) 30

2)

3)

5. 4
1) 100,000
50

2) 30 10,000,000

6. ABC 10

75 a a

7. 2, 200

22
7

8. r ( )v

( 1

) r 3v 3

4

10, 000