Surds, indices, and exponentials (Chapter 4) 109

Example 10 Self Tutor

Write as powers of 2 :

a 16 b 161 c 1 d 4 £ 2 n e

2 m

8

a 16

=2£ 2 £ 2 £ 2

=2^4

b 161

=

1

24

=2¡^4

c 1

=2^0

d 4 £ 2 n

=2^2 £ 2 n

=22+n

e

2 m

8

=

2 m

23

=2m¡^3

2 Write as powers of 2 :

a 4 b^14 c 8 d^18 e 32 f 321

g 2 h^12 i 64 j 641 k 128 l 1281

3 Write as powers of 3 :

a 9 b^19 c 27 d 271 e 3 f^13

g 81 h 811 i 1 j 243 k 2431

4 Write as a single power of 2 :

a 2 £ 2 a b 4 £ 2 b c 8 £ 2 t d (2x+1)^2 e (2^1 ¡n)¡^1

f

2 c

4

g

2 m

2 ¡m

h

4

21 ¡n

i

2 x+1

2 x

j

4 x

21 ¡x

5 Write as a single power of 3 :

a 9 £ 3 p b 27 a c 3 £ 9 n d 27 £ 3 d e 9 £ 27 t

f

3 y

3

g

3

3 y

h

9

27 t

i

9 a

31 ¡a

j

9 n+1

32 n¡^1

Example 11 Self Tutor

Write in simplest form, without brackets:

a

¡

¡ 3 a^2

¢ 4

b

μ

¡

2 a^2

b

¶ 3

a

¡

¡ 3 a^2

¢ 4

=(¡3)^4 £(a^2 )^4

=81£a^2 £^4

=81a^8

b

μ

¡^2 a

2

b

¶ 3

=(¡2)

(^3) £(a (^2) ) 3
b^3

¡ 8 a^6
b^3
4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_04\109CamAdd_04.cdr Tuesday, 14 January 2014 2:28:15 PM BRIAN