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Chapter 3 Indices and surds186

1 Simplify using index form.a 3 × 3 × 3 × 3 b 7 × 7 × 7 × 7 × 7 × 7c 8 × 8 × 8 d 2 × x × x × 3 × xe 3 × y × y × 5 × y × y f 2 × b × a × 4 × b × a × a

2 Copy and complete this table.

x 4 3 2 1 0

2x 23 = 8

3 Copy and complete.a 22 × 23 = 2 × 2 × ______ b x

x

x x x

x

5

3= × × ×

= −

____________ = 2−

c a a a

a

2 3( ) = × × ×

= −

______ ______ d ( ) ___ ___2 2

2

0 0x x× = ×=

Exercise 3F

Unde

rsta

ndin

gFl

uenc

y

4 Simplify using the first index law.a a a5 4× b x x3 2× c b b× 5

d 7 22 3m m× e 2 34 3s s× f t t8 82×

g 15

2p p× h 14

23

4 3c c× i 35

35

ss×

j 2 32 2x y xy× k 3 52 5a b ab× l 3 67 2v w v w×

m 3 5 104 2 4x xy y× × n 2 3 23 4 2 2rs r s r s× × o 4 56 7 2m n mn mn× ×

5 Simplify using the second index law.a x x5 2÷ b a a7 6÷ c q q9 6÷

d b b5 ÷ e yy

8

3 f dd

8

3

g jj

7

6 h mm

15

9 i 2 2 3x y x÷

j 3 5 2 3r s r s÷ ( ) k 6 34 2 2 2p q q p÷ ( ) l 16 87 5 3 4m x m x÷ ( )m

5 2 4

2a ba b

n 82

4

3stt

o 28

5

3vv

p 714

2a bab

q -3

9

4

3

x y

x y r

-8

16

2 3

2

x y

x y

Example 13

Example 14

ISBN 978-0-521-17866-2 Photocopying is restricted under law and this material must not be transferred to another party.

© David Greenwood, Sara Woolley, Jenny Goodman, Jennifer Vaughan, GT Installations, Georgia Sotiriou, Voula Sotiriou 2011 Cambridge University Press

Number and Algebra 187

Flue

ncy6 Simplify using the third, fourth and fifth index laws.

a x5 2( ) b t3 2( ) c 4 2 3a( ) d 5 5 3

y( )

e 4 2 3t( ) f 2 2 2

u( ) g 3 3 3r( ) h 3 4 4

p( )i

ab

2

3

2⎛⎝⎜

⎞⎠⎟

j xy

3

4

3⎛⎝⎜

⎞⎠⎟

k x yz

2 3

4

2⎛⎝⎜

⎞⎠⎟

l u w

v

4 2

2

4⎛⎝⎜

⎞⎠⎟

m 35

2 3fg

⎛⎝⎜

⎞⎠⎟

n 32

2

3

2a bpq

⎛⎝⎜

⎞⎠⎟

o atg

3

4

3

3

⎛⎝⎜

⎞⎠⎟

p 4

3

2 3 4p q

r

⎛⎝⎜

⎞⎠⎟

7 Evaluate the following using the zero power.

a 8 0x b 3 0t c 5 0z( ) d ( )10 2 0ab

e 5 3 3 0g h( ) f 8 50x − g 4 90b − h 7 4 20 0x y− ( )

Example 15

Example 16

Prob

lem

-sol

ving

8 Use appropriate index laws to simplify the following.

a x x x6 5 3× ÷ b x y xy xy2 2÷ ( ) ×

c x n x n xn4 7 3 2× ÷ ( ) d x y x y

x y

2 3 2 4

3 5×

e m w m w

m w

2 3 2

4 3×

f r s r s

r s

4 7 4 7

4 7×

g 9 6

12

2 3 7 5

6x y x y

xy×

h 4 12

24

2 3 2 2

4x y x y

x y×

i 16 4

32

8 7

7 6a b ab

a b×

j 3 2 4 3 2m n mn( ) ×

k -5 32 3 2a b ab( ) × ( ) l 4 32 2 2 4 2 3f g f g fg( ) × ÷ ( )( )

m 4 3

6

2 2 3

2

m n m n

m n

× ( ) n

7 3

7

2 2 2

2

y z yz

yz

( ) ×

( )

o 2 2

4 4

2 2 3

2 7 3

( ) ( )ab a b

ab a b

××

p 2

3

6

2

3 2

4 0

5 2

3 4

m

mn

n

n m

( )( )

×( )

( )-9 Simplify:

a (-3)3 b -(3)3 c (-3)4 d -34

10 Simplify:

a x2 3 2( )( ) b a5 3 7( )( ) c ab

2 3 5⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

ISBN 978-0-521-17866-2 Photocopying is restricted under law and this material must not be transferred to another party.

© David Greenwood, Sara Woolley, Jenny Goodman, Jennifer Vaughan, GT Installations, Georgia Sotiriou, Voula Sotiriou 2011 Cambridge University Press