Cambridge International Mathematics

128 Exponents and surds (Chapter 6)

Example 9 Self Tutor

Express the following in simplest form, without brackets:

a (3a^3 b)^4 b

μ

x^2

2 y

¶ 3

a (3a^3 b)^4

=3^4 £(a^3 )^4 £b^4

=81£a^3 £^4 £b^4

=81a^12 b^4

b

μ

x^2

2 y

¶ 3

=

(x^2 )^3

23 £y^3

=

x^2 £^3

8 £y^3

=

x^6

8 y^3

EXERCISE 6B

1 Simplify using the index laws:

a 23 £ 21 b 22 £ 22 c 35 £ 34 d 52 £ 53

e x^2 £x^4 f a^3 £a g n^4 £n^6 h b^3 £b^5

2 Simplify using the index laws:

a

24

23

b

35

32

c

57

53

d

49

45

e

x^6

x^3

f

y^7

y^4

g a^8 ¥a^7 h b^9 ¥b^5

3 Simplify using the index laws:

a (2^2 )^3 b (3^4 )^3 c (2^3 )^6 d (10^2 )^5

e (x^3 )^2 f (x^5 )^3 g (a^5 )^4 h (b^6 )^4

4 Simplify using the index laws:

a a^5 £a^2 b n^3 £n^5 c a^7 ¥a^3 d a^5 £a

e b^9 ¥b^4 f (a^3 )^6 g an£a^5 h (b^2 )^4

i b^6 ¥b^3 j m^4 £m^3 £m^7 k (a^3 )^3 £a l (g^2 )^4 £g^3

5 Remove the brackets of:

a (ab)^3 b (ac)^4 c (bc)^5 d (abc)^3

e (2a)^4 f (5b)^2 g (3n)^4 h (2bc)^3

i

μ

2

p

¶ 3

j

³a

b

́ 3

k

³m

n

́ 4

l

μ

2 c

d

¶ 5

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Y:\HAESE\IGCSE01\IG01_06\128IGCSE01_06.CDR Monday, 15 September 2008 3:29:53 PM PETER