Cambridge Additional Mathematics

3

5

power,

index or

base exponent

Surds, indices, and exponentials (Chapter 4) 107

Ifnis a positive integer, then an is the product ofnfactors ofa.

an=a|£a£a£{za£ ...... £a}

nfactors

We say thatais thebase, andnis theindexorexponent.

NEGATIVE BASES

(¡1)^1 =¡ 1

(¡1)^2 =¡ 1 £¡1=1

(¡1)^3 =¡ 1 £¡ 1 £¡1=¡ 1

(¡1)^4 =¡ 1 £¡ 1 £¡ 1 £¡1=1

(¡2)^1 =¡ 2

(¡2)^2 =¡ 2 £¡2=4

(¡2)^3 =¡ 2 £¡ 2 £¡2=¡ 8

(¡2)^4 =¡ 2 £¡ 2 £¡ 2 £¡2=16

From the patterns above we can see that:

Anegativebase raised to anoddindex isnegative.

Anegativebase raised to anevenindex ispositive.

EXERCISE 4B

1 List the first six powers of:

a 2 b 3 c 4

2 Copy and complete the values of these common powers:

a 51 =::::, 52 =::::, 53 =::::, 54 =::::

b 61 =::::, 62 =::::, 63 =::::, 64 =::::

c 71 =::::, 72 =::::, 73 =::::, 74 =::::

3 Simplify, then use a calculator to check your answer:

a (¡1)^5 b (¡1)^6 c (¡1)^14 d (¡1)^19 e (¡1)^8 f ¡ 18

g ¡(¡1)^8 h (¡2)^5 i ¡ 25 j ¡(¡2)^6 k (¡5)^4 l ¡(¡5)^4

4 Use your calculator to find the value of:

a 47 b 74 c ¡ 55 d (¡5)^5 e 86 f (¡8)^6

g ¡ 86 h 2 : 139 i ¡ 2 : 139 j (¡ 2 :13)^9

5 Use your calculator to find the values of:

a 9 ¡^1 b

1

91

c 6 ¡^2 d

1

62

e 3 ¡^4 f

1

34

g 170 h (0:366)^0

What do you notice?

6 Consider 31 , 32 , 33 , 34 , 35 .... Look for a pattern and hence find the last digit of 3101.

7 What is the last digit of 7217?

B Indices

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_04\107CamAdd_04.cdr Thursday, 3 April 2014 5:07:26 PM BRIAN