Mathematics Index Laws Stage 6 Year 11 Press

  • Slides: 9
Download presentation
Mathematics Index Laws Stage 6 - Year 11 Press Ctrl-A ©G Dear 2010 –

Mathematics Index Laws Stage 6 - Year 11 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use 1

Index Laws 1. Multiplication am x an = am+n e. g. 23 x 25

Index Laws 1. Multiplication am x an = am+n e. g. 23 x 25 = 23+5 = 28 2. Division am ÷ an = am-n e. g. 37 ÷ 35 = 37 -5 = 32 3. Powers of Powers (am)n = amxn e. g. (72)3 = 72 x 3 = 76 2

Index Laws A amxan = am+n B am÷an = am-n C (am)n = amxn

Index Laws A amxan = am+n B am÷an = am-n C (am)n = amxn a) 39 x 37 = 316 a) 39÷ 37 = 32 a) (39)7 = 363 b) 28 x 23 = 25 b) 28÷ 23 = 25 b) (23)3 = 29 c) 57 x 56 = 513 c) 57÷ 56 = 5 c) (57)6 = 542 d) 25 x 23 = 28 d) 25÷ 23 = 22 d) (25)3 = 215 e) 76 x 73 = 79 e) 76÷ 73 = 73 e) (76)3 = 718 3

Index Laws 3. Powers of a Product (ab)n = an bn Eg (3 x

Index Laws 3. Powers of a Product (ab)n = an bn Eg (3 x 4)2 = 32 x 42 4. Powers of a Quotient n a an = n b b E. g. 3 2 23 = 3 5 5 4

A Index Laws an a = bn b (ab)n = an bn a) (2

A Index Laws an a = bn b (ab)n = an bn a) (2 x 3)7 =27 x 37 b) (5 x 2)3 =53 x 23 c) (9 x 5)6 =96 x 56 d) (2 x 6)3 =23 x 63 e) (3 x 7)3 =33 x 73 B n a) 4 4 2 2 = 4 3 3 b) = 2 11 11 12 5 125 c) = 5 13 13 5

Index Laws 5. Zero Indicies a 0 = 1 Eg 780 = 1 6.

Index Laws 5. Zero Indicies a 0 = 1 Eg 780 = 1 6. Negative Indicies 1 -n a = n 1 a -2 Eg 3 = 2 3 6

A a 0 Index Laws = 1 a-n a) 30 = 1 b) 520

A a 0 Index Laws = 1 a-n a) 30 = 1 b) 520 = 1 c) 90 x 50 = 1 d) 2 x 60 = 2 e) 30 x 7 B = 7 1 = n a 1 a) 3 = 4 3 -4 1 b) 5 = 6 5 -6 1 c) 7 = 3 7 -3 7

Index Laws 7. Fractional Indices 1 an = n a E. g. 1 3

Index Laws 7. Fractional Indices 1 an = n a E. g. 1 3 4 = 3 4 8. Mixed Fractional Indicies m an = n a m E. g. 3 a 2 = 2 a 3 9. Negative Mixed Fractional Indices 1 -2 -m = 1 n = 3 m E. g. a n m a n a a 8

Index Laws A 1 an B =n a 1 3 3 a) 5 =

Index Laws A 1 an B =n a 1 3 3 a) 5 = Answer 5 1 2 b) 7 = 1 5 c) 3 = 7 Answer 5 Answer 3 m an n = C a 2 3 a) 4 = 3 2 b) 2 = 4 5 c) 7 = -m an m 2 3 Answer 4 5 Answer 7 = n 1 a -1 4 a) 4 = -2 3 b) 6 = m 1 Answer 3 4 1 Answer 6 9