Fractional and Law of Indices

8/8/2019 Fractional and Law of Indices

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FRACTIONAL AND LAW OF INDICES

PANITIA MATEMATIK SMAKT

TITTLE:

INDICES

PN MAZLIN BTE IDRIS



1 Given that 25 2

1

is equal to the

square root of 25, what is 100 2

1

equal

to?

A 100 cubed

B 100 squared

C Cube root of 100

D Square root of 100

2. Which of the following is a number witha fractional index ?

A 4 3

1

B3

4

1

C 4 – 4

D 4 5

3n

m

a

a=

. nma

−

. nma

+

. nma

×

. nma

÷

4 n

m

a=

nm

a

−

n

m

a

a

n ma

( )nm a

5 Express 4

3

625in the form of n m

a

3 4625

( ) 43

625×

4625

4 3625

6 Evaluate 3

2

27.

A 3

B 6

C 9

D 18

7 Evaluate

A 5

B 10

C 20

D 25

8 Which of the following is not equal to

4?

A

B

C

D

9 Given = X , find the value

of p.

A

B

C

D

10 =

A



B

C

D 12

11 =

A 4

B 3

C 6

D 5

12 =

A 3

B 4

C 2

D 1

13 Express in root form

A

B

C

D

14 Express in index form

A

B

C

D

15 =

A

B

C

D

16 Find the value of

A 81

B 9

C 3

D 27

17 Simplify of

A

B

C

D

18 Simplify of

A

B

C

D

19 Simplify of

A

B

C

D

20 Simplify

A

B

C

D

21 =

A -1



B 0

C 1

D 5

22 Which of the following does not equal

?

A

B

C

D

23 =

A

B

C

D

24

A

B

C

D 0

25

A

B

CD

26 Given that , find the

value of p.A 4B 5C 6D 7


A 5B 10

C 25D 125


A

B

C

D


A

B

C

D

30 Simplify

A

B

C

D

31 Simplify

A

B

C

D

32 =

A 1B 2C 5

D 25

33

A 4B 16C 24D 36


A 9B 12



C 14D 16

35 Evaluate

A 8B 16C 20D 25


A

B

C 3D 9


A

B

C

D


AB

C 3D 9

39 SimplifyA

B

C

D

40 Given that , thenA 2B 4C 8D 16

41 Simplify

A

B

C

D

42 Simplify

AB

C

D 6


A

B

C

D

44 Given that , thenA 2B 3C 4D 8

45 Given that , find the value of

A 2 C 3B 4 D 5

46 Simplify

AB

C

D

47 Simplify

A

B

C

D

48

A 35B 70C 105D 135

49 Simplify

A

B

C



D


A 9B 12

C 14D 16

51

A -1 C 0B 1 D 2

52 Given that 216 = , thenA 216 C 4B 6 D 3

53 =

A 1 C 2B 0 D 3

54 =

A

B

CD

55 Given that + , findthe value of p.A 5 C 16B 9 D 25

56 Give that calculate the value

of .A 5 C -5B 11 D 8

57 Given that

Calculate the value of A 4 C 5B 3 D 6


A 12 C 160B 144 D 11

59 Given that find the value of

A 7 C 1B 5 D 6

60 Simplify

A C

B D

61 If = , then

A 27 C 3

B D

62 Given tha

A 3 C 4B 2 D 6

63 Given that

A 5 C 4B 0 D 1

64 Given that

A 6 C 8B 4 D 7

65 Given

A 1 C 2B 3 D 4

SUBJECTIVE

1 Simplify



2 Simplify

3 Simplify

4 Simplify

5 Simplify

6 Find the value of

7 Simplify

8 Evaluate

9 Find the value of


11 Find the value


13

14

15 =

16 =

17 =

18 Find =

19 Find =

20 =

21 =

22 =

23 Simplify

24 =



25 =

26

27

28

29

30 =

31

32 Simplify


34 =

35 Simplify

36 Given that , find the value

of p.

37 Evaluate


39 Simplify


41 Simplify

42

43

44

45 =

46



47



50 =

51

52 =

53 =

54 216 = , then

55 If , find the value of m.

56 Give that calculate the

value of .

57 Given that

Calculate the value of

58 Given

59 Given that find the value

of .

60 Given that , find the value

of

61 Simplify

62 Given that

63 Given that

64 Given that . Find the value

of

65 Given . Find the value

of .

NEGATIVE INDICES AND LAW OF INDICES

OBJECTIVE QUESTIONS.



1. Simplify ( 8 x 3 -6 ) 1/ 3 ÷ ( 2 3 x 3 -4 )

A. ¼B. 1/9

C. 4/9D. 9/4

2. Simplify ( m 2 ) 4 ÷ m 5

A. mB. m 3

C. m 11 D. m 13

3. Simplify ( 4m-1 n1/2 )2 x 9

32

p

pm

A. 3

4

p

n

B. 6

16

p

n

C. 3

4

p

mn

D. 6

216

p

mn

4 Seven to the power of four is equal to 7× 7 × 7 × 7.

What is five to the power of three?

A 3 × 5

B 3 × 3 × 3 × 3 × 3

C 5 × 5 × 5

D 7 × 7 × 7

5 In the number 52 , 2 is the base.

What is the base in the number 68 ?

A 2

B 5

C 6

D 8

6 Six raised to the fifth power is writtenas . Seven raised to the fourth power iswritten as

A 47

B 57

C 46

D 74

7 Given that 25 2

1

is equal to the square

root of 25, what is 100 2

1

equal to?

D 100 cubed

E 100 squared

F Cube root of 100

G Square root of 100

8 Two numbers, b to the power of m andb to the power of n, when multiplied isequal to b to the power of m plus n.

What is the product of 2 to the power of 4 and 2 to the power of 3?

A 2 4 + 3

B 2 4 – 3

C4 3 + 2

D 4 3 – 2

9 Which of the following is a number witha fractional index ?

E 4 3

1

F3

4

1

G 4 – 4

H 4 5

10 Express 5 4 in the form of repeated

multiplication.

A 4 × 4 × 4 × 4

B 5 × 5 × 5 × 5



C 4 × 4 × 4 × 4 ×4

D 5 × 5 × 5 × 5 × 5

11. When a number is expressed in the

form of a m , m is known as the

index

base

factor

root

12. 81 is written in the form of 3 4 .

3 is known as the ________.

base

factor

index

root

13 When a number is written as a n , the

form a n is

set notation

index notation

scientific notation

expanded notation

14 Given that 52h × 16

3h =16

32 hhm××× , what is the value of

m ?

2

3

5

16

15. =×÷435

aaa

A a

5

+ 3 + 4

a5 + 3 – 4

a5 – 3 + 4

a5 – ( 3 + 4)

16 Which of the following is true about the

number 10

6 ?

6 is the power.

6 is the index

10 is the base

10 is the index

17n

m

a

a=

A. nma

−

B. nma

+

C. nma

×

D. nma

÷

18 n

m

a=

A. nma−

B.n

m

a

a

C. n ma

D. ( )nm a

19 Express 4

3

625in the form of n m

a

A. 3 4625

B. ( ) 43

625×

C. 4625

D. 4 3625

20 ( 257

257

+



257

×

257

−

257

÷

21 Which of the following is equal to 8 p ?

( )80 p

( )62 p

4 p ×

2 p

4 p ×

4 p

22

( )

73 p ÷ 9−

p =

9)(73 −−×

p

9)(73 −+×

p

9)(73 −÷×

p

9)(73 −××

p

23 Which of the following is equivalent to7

3

6

ba

?

A3

76

b

a×

B3

76

b

a +

C73

76

×

×

b

a

D73

76

+

+

b

a

24 Given that 35− k

5× = 45 , find the

value of k .

A 7

B 1

C – 1

D – 7

25 Simplify 424r

26

−

÷ r .

A 84

−r

B 24

−r

C 24r

D 64r

26 Evaluate 3

2

27.

A 3

B 6

C 9

D 18

27 Simplify ( )392b

A 278b

B 128b

C 272b

D 122b

28 Simplify ( )3443 × 6

3÷

A 3643 ×

B 436 ×

C 3243 ×

D 3243 ×−

29. a0 x a4 x 3a-3 =

A. 3a7

B. 3aC. 3a-1

D. 3

30. Given that ( 2

1

y)3

= ym , then m =

A. -6B. 1



C. 5D. 6

31 . If (

3

1)-3 = p , the

value of p =

A.27

1

B.9

1

C. 1D. 27

32. ( ef 2 )3 ÷ e5 f 2 =

A. e-4 f 4

B. e-2 f 3

C. e5 f 4

D. e-2 f 4

33. Given that 81 4

3=

w , then w =

A. 3B. 27C. 9

D. 108

34. Given that 2 x 2-3

= y , the value of y =

A. 4-3

C. 22

B.8

1

D.4

1

35. Given that w-3 x ( w8) 4

1= p , then p =

A. w-5

B. w-1

C. w

D. w

5

36

4

)5(4 42

1

2

3

x =

A. 50

B. 37.5C. 5D. 2

37. u-1 v2 ÷ ( uv-3 )2 =

A. u-2 v8 B. u-1 v-3

C. u2

1−v 3

1−

D. u-3 v8

38. If 3 4

9÷ 3 4

1= h , h =

A. 3

B. 6C. 9D. 2

Repeated Multiplication.

A. Expand the following.

1) 23 2) 54

3) 65 4) 77

5) -23 6) -54

7) (8

1)3 8) (-

4

1)7

9) (0.3)3 10) (5.2)4

11) (-0.2)3 12) (- 0.05)3



13) a3 14) p4

15) y3

16) h7

17) - f 3 18) - b4

19) (2x)2 20) ( 5p)7

21) (-2r)3 22) ( 6w)4

23) (8

1y)3 24) (-

4

1k)7

25) (3 g)3 26) (5e)4

2.2 Index Notation.

B. Express each of the following in simple

index notation.

1) ( 22)2 2) ( 33)2

3) ( 53 )4 4) ( 82 )4

5) ( -22)2 6) ( -33)2

7) ( a3 )4 8) ( p2 )4

9) ( b4 )2 10) ( p7 )6

11) ( -x3 )5 12) (- y2 )3

13) ( 2a2)2 14) ( 3b3)2

15) ( -5a3 )4 16) ( -6p2 )4

17) ( 2x2)2 18) ( 3y3)2

19) (4

1 3 )5 20) (

3

1 6 )7

21) (-2

16)2 22) (-

5

1 2)2

5.3 Multiplication of Numbers in IndexNotation.

C. Simplify each of the following.

1) 24 x 22 2) 32 x 35

3) 34 x 32 4) 52 x 55

5) -45 x -43 6) -62 x -69

7) y3

x y6

8) b6

x b5

9) a3 x a6 10) k6 x k5

11) -y3 x -y6 12) -b6 x -b5





13) m8 ÷ (m2)3

14) n6 ÷( n2 )2

15) (a3)4 ÷a7

16) ( b3 )2

x b5

17) g2 x( g4 )2

18) 46 ÷ ( 42

)2

19) -m8 ÷(-m2)3

20) -n6 ÷ (-n2 )2

21) (-a3)4 ÷-a7

22) m8 ÷ (m2)3

23) n6 ÷( n2 )2

24) (a3)4 ÷a7

25) ( b3 )2

x b5

26) g2 x( g4 )2

27) 46 ÷ ( 42

)2

28) ( a2b2

)3 x a2

29) ( a4b2)2 x b3

30) ( a2 b2)2

x a2b6

31) 3m8 ÷ 32) 18n6 ÷ 33) (32a3)4 ÷

( m2)3 (3n2 )2 32a7

34) (3g3 )2 x g5

35) 3g2 x(3g4 )2

36) 3g6 ÷(32g2 )2

37) ( 32a2

)3 x 32

38) ( 24b2)2 x 23

39) ( 52c2 )2

x 56

5.6 Fractional Indices.

F. Simplify each of the following.

1) ( 43 ) 31

2) ( 5 2

1

)2

3) (x 4

3

)4 4) (d5) 5

4

5) (y 3

1

)6 6) ( n 4

3

)12

7) ( 4a2 ) 2

18) ( 16 w4 ) 2

1





7)

4

4

3

2

22

× 8)

25

125625

2

1

3

1

4

1 −

×

9)2

1

2

1

520

1000

×

10) ( ) 4816 31

4

3

÷×

11)

( )

( )

25

55

3

1

8

4

1

3

12-

−

×

12)

( )

( )

25

55

3

1

8

4

1

3

12-

−

×

13) 5

55.

1

2

-1−

× 14)

2321635

1

2

3

−×÷

15)3

-2

381

327−

×

× 16)

PMR QUESTIONS

PAPER 2

INDICES

This question paper consists of 15 questions.

Answer all questions. Write your answers

clearly in the space provided. Show your

working. The usage of calculator is not

allowed.

1) Simplify =÷×−35

mmm 2) Simplify

3) Simplify ( )72 f e 3 =

Answer :

4) Simplify

Answer :

5) Simplify ( ) 51

15 x ×

4

2

1

3

x =

Answer :

6) Find the

=

Answer :



7) Simplify 2

1

3

1

26484 ÷×

=

Answer :

8) Simplify

Answer :

9) Simplify ( ) ( ) f eef e 92332 ÷× =

Answer :

10) Simplify

Answer :

11) Simplify ( ) ( ) 744252h g h gh ÷×

Answer :

12) Simplify

Answer :

13) Given that 82 2 =+ x , find the

value of x.

Answer :

14) Given

value of x.

Answer :

17) Simplify ( ) ( ) 963442 k mk mk ÷× = 18) Simplify

19)Simplify

2

4

−k

k x k

20) 3 2x-1

of x

21) Find the value of 3/2

2/1

8

3x 121/2

22) Given thatof x

23) Simplify ( 2mk 2 ) 4 x ( k 2 ) 3 ÷ m 5

k9

24) Simplify (

25) Find the value 2 ÷ 2 -3 26) Simplify 1

27) Simplify ( m -1 h 3 ) 3 ÷ m 2 h -228) Simplify (

29) Find the value of 2 5 x ( 2 -3 ) 230)Given 23

value of x.

31) Find the value of 3 2 x 18 ½ x 2 3/2 32) Given that



33) Simplify( )52

24

ph

ph−

= 34) Simplify

35) Simplify ( )72 f e 3 =36) Simplify

37) Find the value of 3 4− × 9 3 ÷13− =

38) Simplify

39) Simplify 2

1

53

1

4264 ÷×= 40) Simplify

41) Simplify ( ) 51

15 x ×

4

21

3

x =

42)

Giv

( ) ( )

pof valuethecalculate

,1628Given that1

=− p

theFind

xof valuethecalculate

,556255Given that 31x×=×

−+ x

2793If 24-k =÷

( )( )n.of valuethefind

,222Given that 21-3n n= 5Given that 2x

( ) 355x pif xof valuetheFind p=2

1 216If

m

1- =÷

Given that 2564 1 =− x Calculate the

value of x

7Given that 4×

Given that )3)(3(3212 x x

=−

Calculate the value of x

INDICESt

`



( )

( ) ( )

( )

( ) ( )

( )

( )

( ) 95231-

460

3

32521-

2315323

64352-

53224-

2332

235

82pxv.

m xiii.

2

14hk xi.

p ix.

x vii.

2x v.

42a iii.

25100m i.

followingtheof eachSimplifyc)

q pq

m

hk h

qq pq

y x y

x x

bab

nmn

÷

÷

÷×

×÷

÷

÷×

÷

÷

−

−−−

−−−

−−

−

−−−−

−

−

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Fractional and Law of Indices