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

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2 1. Multiplication a m x a n = a m+n e.g. 2 3 x 2 5 =2 3+5 =2828 2. Division a m ÷ a n = a m-n e.g. 3 7 ÷ 3 5 =3 7-5 =3232 3. Powers of Powers (a m ) n = a mxn e.g. (7 2 ) 3 =7 2x3 = 7676 Index Laws

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3 a) 3 9 x3 7 =3 16 b) 2 8 x2 3 =2 5 c) 5 7 x5 6 =5 13 d) 2 5 x2 3 =2 8 e) 7 6 x7 3 =7 9 a m xa n = a m+n a m ÷a n = a m-n (a m ) n = a mxn a) 3 9 ÷3 7 =3 2 b) 2 8 ÷ 2 3 =2 5 c) 5 7 ÷ 5 6 =5 d) 2 5 ÷ 2 3 =2 2 e) 7 6 ÷ 7 3 =7 3 a) (3 9 ) 7 =3 63 b) (2 3 ) 3 =2 9 c) (5 7 ) 6 =5 42 d) (2 5 ) 3 =2 15 e) (7 6 ) 3 =7 18 ABC

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4 4. Powers of a Quotient 3. Powers of a Product (ab) n = a n b n Eg (3 x 4) 2 = 3 2 x 4 2 Index Laws anbnanbn abab n = 23532353 2525 3 = E.g.

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5 Index Laws a) (2x3) 7 =2 7 x3 7 b) (5x2) 3 =5 3 x2 3 c) (9x5) 6 =9 6 x5 6 d) (2x6) 3 =2 3 x6 3 e) (3x7) 3 =3 3 x7 3 a) = b) = c) = AB (ab) n = a n b n anbnanbn abab n = 2323 4 3 11 2 12 13 5 2323 4 3 11 2 12 13 5 4 2 5

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6 6. Negative Indicies 5. Zero Indicies a 0 = 1 Eg 78 0 =1 a -n = Eg 3 -2 = Index Laws 1an1an 132132

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7 a) 3 0 =1 b) 52 0 =1 c) 9 0 x5 0 =1 d) 2x6 0 =2 e) 3 0 x7 =7 a) 3= b) 5= c) 7= AB 1313 1515 1717 4 6 3 a 0 = 1 a -n = 1an1an -4 -6 -3

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

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9 Index Laws ABC a n = a 1 n = a -m n a n m 1 = a m n a n m a) 5 = b)7= c)3= 5 3 1313 1212 1515 73 5 a) 4 = b)2= c)7= 4 3 2323 3232 4545 27 5 a) 4 = b)6= 4 3 4 -2 3 6 2 3 4 1 1 Answer

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