Cambridge Additional Mathematics

110 Surds, indices, and exponentials (Chapter 4)

6 Write without brackets:

a (2a)^2 b (3b)^3 c (ab)^4 d (pq)^3 e

³m

n

́ 2

f

³

a

3

́ 3

g

³

b

c

́ 4

h

³

2 a

b

́ 0

i

³

m

3 n

́ 4

j

³

xy

2

́ 3

7 Write the following in simplest form, without brackets:

a (¡ 2 a)^2 b (¡ 6 b^2 )^2 c (¡ 2 a)^3 d (¡ 3 m^2 n^2 )^3

e (¡ 2 ab^4 )^4 f

μ

¡ 2 a^2

b^2

¶ 3

g

μ

¡ 4 a^3

b

¶ 2

h

μ

¡ 3 p^2

q^3

¶ 2

i

(2x^2 y)^2

x

j

(4a^2 b)^3

2 ab^2

k

(¡ 5 a^6 b^3 )^2

5 b^8

l

(¡ 2 x^7 y^4 )^3

4 x^3 y^15

Example 12 Self Tutor

Write without negative exponents:

a¡^3 b^2

c¡^1

a¡^3 =^1

a^3

and^1

c¡^1

=c^1

)

a¡^3 b^2

c¡^1

=

b^2 c

a^3

8 Write without negative exponents:

a ab¡^2 b (ab)¡^2 c (2ab¡^1 )^2 d (3a¡^2 b)^2 e a

(^2) b¡ 1
c^2
f
a^2 b¡^1
c¡^2
g
1
a¡^3
h
a¡^2
b¡^3
i
2 a¡^1
d^2
j
12 a
m¡^3

Example 13 Self Tutor

Write

1

21 ¡n

in non-fractional form.

1

21 ¡n

=2¡(1¡n)

=2¡1+n

=2n¡^1

9 Write in non-fractional form:

a^1

an

b^1

b¡n

c^1

32 ¡n

d a

n

b¡m

e a

¡n

a2+n

10 Simplify, giving your answers in simplest rational form:

a

¡ 5

3

¢ 0

b

¡ 7

4

¢¡ 1

c

¡ 1

6

¢¡ 1

d

33

30

e

¡ 4

3

¢¡ 2

f 21 +2¡^1 g

¡

(^123)
¢¡ 3
h 52 +5^1 +5¡^1
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\110CamAdd_04.cdr Tuesday, 14 January 2014 2:28:18 PM BRIAN