Cambridge International Mathematics

126 Exponents and surds (Chapter 6)

Example 4 Self Tutor

Find, using your calculator: a 65 b (¡5)^4 c ¡ 74

Answer

a Press: 6 ^ 5 ENTER 7776

b Press: ( (¡) 5 ) ^ 4 ENTER 625

c Press: (¡) 7 ^ 4 ENTER ¡ 2401

EXERCISE 6A.2

1 Simplify:

a (¡1)^4 b (¡1)^5 c (¡1)^10 d (¡1)^15 e (¡1)^8 f ¡ 18

g ¡(¡1)^8 h (¡3)^3 i ¡ 33 j ¡(¡3)^3 k ¡(¡6)^2 l ¡(¡4)^3

2 Simplify:

a 23 £ 32 £(¡1)^5 b (¡1)^4 £ 33 £ 22 c (¡2)^3 £(¡3)^4

3 Use your calculator to find the value of the following, recording the entire display:

a 28 b (¡5)^4 c ¡ 35 d 74 e 83 f (¡7)^6

g ¡ 76 h 1 : 0512 i ¡ 0 : 62311 j (¡ 2 :11)^17

Notice that: ² 23 £ 24 =2£ 2 £ 2 £ 2 £ 2 £ 2 £2=2^7

²

25

22

=

2 £ 2 £ 2 £ 2 £ 2

2 £ 2

=2^3

² (2^3 )^2 =2£ 2 £ 2 £ 2 £ 2 £2=2^6

² (3£5)^2 =3£ 5 £ 3 £5=3£ 3 £ 5 £5=3^252

²

μ

2

5

¶ 3

=

2

5

£

2

5

£

2

5

=

2 £ 2 £ 2

5 £ 5 £ 5

=

23

53

These examples can be generalised to the exponent or index laws:

² am£an=am+n Tomultiplynumbers with thesame base, keep the base

andaddthe indices.

²

am

an

=am¡n, a 6 =0 Todividenumbers with thesame base, keep the base

andsubtractthe indices.

² (am)n=am£n Whenraisingapowerto apower, keep the base and

multiplythe indices.

² (ab)n=anbn The power of a product is the product of the powers.

²

³a

b

́n

=

an

bn

, b 6 =0 The power of a quotient is the quotient of the powers.

B EXPONENT OR INDEX LAWS [1.9, 2.4]

1

1

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Y:\HAESE\IGCSE01\IG01_06\126IGCSE01_06.CDR Thursday, 18 September 2008 12:14:38 PM PETER