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MultiplicationMultiplicationIndex NotationIndex Notation

Stage 6 - Year 11Stage 6 - Year 11

General MathematicsPreliminary

2

Multiplication 1/1

crossedwith

aProduce

a

Horse x Donkey = Muleor

Horse x Donkey = Horse/Donkey

i.e. h x d = hd

3

Index Notation – Index Form

1. a7 =a x a x a x a x a x a x a

2. b3 = b x b x b

3. a2b3 =a x a x b x b x b

4. 3c4d3 = 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 =m4

2. b x b x b x b x b x b x b =b7

3. 3 x a x a x 4 x b x b x b =12a2b3

4. 3 x f x 2 x f x 4 x f = 24f3

5

Index Laws – Multiplication

ax x ay = ax+y

1. b2 x b5 = b7 2. m18 x m2 =m20

3. h8 x h2 x h5 = h15

4. 2a3 x 3a4 = 6a7

5. 4m8 x 3m3 x 5m =60m12

6

Index Laws – Division

ax ÷ ay = ax-y

1. b12 ÷ b5 = b7 2. m8 ÷ m12 =m-4

3. h8 ÷ h2 ÷ h5 = h1

4. 24a9 ÷ 3a4 =8a5

5. 48m8 ÷ 12m2 ÷ m =4m5

= h

7

Index Laws – Powers

(ax)y = axy

1. (b12)5 = b60 2. (m8)2 = m16

3. (3h8)2 = (3)2 (h8)2 =

4. (2a9b4)3 = (2)3 (a9)3 (b4)3

5. (3x3y5z)4 = (3)4 (x3)4 (y5)4 (z1)4

9 h16

= 81x12y20 z4

= 8a27b12