Cambridge Additional Mathematics

112 Surds, indices, and exponentials (Chapter 4)

Example 14 Self Tutor

Write as a single power of 2 :

a^3

p

2 b p^1

2

c^5

p

4

a^3

p

2

=2

1

3

b

1

p

2

=

1

2

1

2

=2

¡^12

c^5

p

4

=(2^2 )

1

5

=2

2 £^15

=2

2

5

EXERCISE 4D

1 Write as a single power of 2 :

a^5

p

2 b

1

p 52 c 2

p

2 d 4

p

2 e

1

p (^32)
f 2 £^3
p
2 g
4
p
2
h (
p
2)^3 i
1
p 316 j
1
p
8
2 Write as a single power of 3 :
a^3
p
3 b
1
p 33 c
p (^43) d 3 p 3 e 1
9
p
3
3 Write the following in the form ax whereais a prime number andxis rational:
a^3
p
7 b^4
p
27 c^5
p
16 d^3
p
32 e^7
p
49
f
1
p 37 g
1
p 427 h
1
p 516 i
1
p 332 j
1
p (^749)
4 Use your calculator to evaluate:
a 3
3
(^4) b 2
7
(^8) c 2 ¡
1
(^3) d 4 ¡
3
(^5) e^4
p
8
f^5
p
27 g p 31
7

Example 15 Self Tutor

Without using a calculator, write in simplest rational form:

a 8

4

(^3) b 27 ¡
2
3
a 8
4
3
=(2^3 )
4
3
=2
3 £^43
f(am)n=amng
=2^4
=16
b 27
¡^23
=(3^3 )
¡^23
=3
3 £¡^23
=3¡^2
=^19
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\112CamAdd_04.cdr Tuesday, 14 January 2014 2:28:23 PM BRIAN