Cambridge International Mathematics

124 Exponents and surds (Chapter 6)

Example 1 Self Tutor

Find the integer equal to: a 34 b 24 £ 32 £ 7

a 34

=3£ 3 £ 3 £ 3

=9£ 9

=81

b 24 £ 32 £ 7

=2£ 2 £ 2 £ 2 £ 3 £ 3 £ 7

=16£ 9 £ 7

= 1008

Example 2 Self Tutor

Write as a product of prime factors in index form:

a 144 b 4312

a 2 144

2 72

2 36

2 18

3 9

3 3

1

) 144 = 2^4 £ 32

b 2 4312

2 2156

2 1078

7 539

7 77

11 11

1

) 4312 = 2^3 £ 72 £ 11

EXERCISE 6A.1

1 Find the integer equal to:

a 23 b 33 c 25 d 53

e 22 £ 33 £ 5 f 23 £ 3 £ 72 g 32 £ 52 £ 13 h 24 £ 52 £ 11

2 By dividing continuously by the primes 2 , 3 , 5 , 7 , ..... , write as a product of prime factors in index

form:

a 50 b 98 c 108 d 360

e 1128 f 784 g 952 h 6500

3 The following numbers can be written in the form 2 n. Findn.

a 32 b 256 c 4096

4 The following numbers can be written in the form 3 n. Findn.

a 27 b 729 c 59 049

5 By considering 31 , 32 , 33 , 34 , 35 .... and looking for a pattern, find the last digit of 333.

6 What is the last digit of 777?

7 Findnif:

a 54 =n b n^3 = 343 c 11 n= 161 051 d (0:6)n=0:046 656

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Y:\HAESE\IGCSE01\IG01_06\124IGCSE01_06.CDR Wednesday, 17 September 2008 9:33:15 AM PETER