1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Multiplication Index Notation Stage 6 - Year 11 General Mathematics Preliminary

2 Multiplication 1/1 crossed with a Produce a Horse x Donkey = Mule or H orse x D onkey = H orse/ D onkey i.e. h x d = hd

3 Index Notation – Index Form 1. a 7 = a x a x a x a x a x a x a 2. b 3 = b x b x b 3. a 2 b 3 = a x a x b x b x b 4. 3c 4 d 3 = 3 x c x c x c x c x d x d x d

4 Index Notation – Index Form 1. m x m x m x m = m4m4 2. b x b x b x b x b x b x b =b7b x a x a x 4 x b x b x b =12a 2 b x f x 2 x f x 4 x f = 24f 3

5 Index Laws – Multiplication a x x a y = a x+y 1. b 2 x b 5 =b7b7 2. m 18 x m 2 =m h 8 x h 2 x h 5 =h a 3 x 3a 4 =6a m 8 x 3m 3 x 5m =60m 12

6 Index Laws – Division a x ÷ a y = a x-y 1. b 12 ÷ b 5 =b7b7 2. m 8 ÷ m 12 =m h 8 ÷ h 2 ÷ h 5 =h1h a 9 ÷ 3a 4 =8a m 8 ÷ 12m 2 ÷ m =4m 5 = h

7 Index Laws – Powers (a x ) y = a xy 1. (b 12 ) 5 =b (m 8 ) 2 =m (3h 8 ) 2 =(3) 2 (h 8 ) 2 = 4. (2a 9 b 4 ) 3 =(2) 3 (a 9 ) 3 (b 4 ) 3 5. (3x 3 y 5 z) 4 =(3) 4 (x 3 ) 4 (y 5 ) 4 (z 1 ) 4 9 h 16 = 81x 12 y 20 z 4 = 8a 27 b 12