# The Laws Of Surds.

Algebraic Operations www.mathsrevision.com S4 Credit Adding / Sub Indices Negative Indices Fraction Indices Harder Indices www.mathsrevision.com Starter Questions www.mathsrevision.com S4 Credit 1. Simplify the following fractions : 7 7 (a) b b a a (b) 2a 2d 2. Simplif y 2c(4 - c) - 5(4 +c)

3. Multiply out (x +1)(x - 5) www.mathsrevision.com Algebraic Operations www.mathsrevision.com S4 Credit Learning Intention Success Criteria 1. To explain how to multiply and divide indices by adding / subtracting powers. www.mathsrevision.com 1. Understand basic rules for indices. 2. Simplify indices. Indices www.mathsrevision.com S4 Credit an is a short hand way of writing

a x a x a . (n factors) a is called the base number and n is called the index number Calculate : 23 x 22 Calculate : 25 = 32 2x2x2 x2x2= 32 Can you spot the connection ! www.mathsrevision.com Indices www.mathsrevision.com S4 Credit 4 x 4 x 4 4 x 4= 4 Calculate : 43 42 Calculate : 41 = 4 Can you spot the connection ! am x an = a(m + n) simply add

powers am an = a(m - n) powers simply subtract www.mathsrevision.com What Goes In The Box ? www.mathsrevision.com S4 Credit b3 x b5 = b8 2m4 x 3m33= 6m3 3f4 x 3g5 = 4 5 9f g 7 y9 y5 = y4

10s23 2s11 = 5s12 www.mathsrevision.com 8a3 x 7a0 = 56a3 Indices www.mathsrevision.com www.mathsrevision.com S4 Credit Now try MIA Ex 2.1 & Ex3.1 Ch9 (page 176) 10 Feb 2020 Created by Mr Lafferty Maths Dept Starter Questions www.mathsrevision.com S4 Credit 1. Simplify the following fractions :

u 5 (a) 3 10 u a a (b) 2a 2d 2 2. Factorise 3x 9x 3. Factorise x2 +3x +2 4. Simplif y 4d3 6d2 www.mathsrevision.com Algebraic Operations www.mathsrevision.com S4 Credit Learning Intention Success Criteria 1. To explain how to hand fractional indices of powers. 1. Understand basic rules for fractional indices.

2. Simplify fractional indices. www.mathsrevision.com Fractions as Indices www.mathsrevision.com S4 Credit More Rules a = aaa =1 2 5 a aaaaa a 3 By the division rule 3 a 3-5 -2 =a =a 5 a www.mathsrevision.com 1 -n =a n

a Fractions as Indices www.mathsrevision.com S4 Credit More Rules a =aaaaa = 1 5 a aaaaa 5 5 a 5 a 5-5 =a 0 =a www.mathsrevision.com 0

a =1 What Goes In The Box ? www.mathsrevision.com S4 Credit Re-write each with positive indices 9 a-3 9a3 5d-4 5 d4 w6 -2 -3 w w w1 1 7 4m-3 2h 7m3

4 2 h -1 www.mathsrevision.com 6a6 2a3 3a3 1 Fractions as Indices www.mathsrevision.com S4 Credit More Rules 5 3 a 3 5 a 5 5

5 5 +5 +5 3 3 3 3 =a a a =a 15 a 3 =a a a a a 3 +3 +3 +3 +3 =a 15 a m n www.mathsrevision.com

mn (a ) =a What Goes In The Box ? www.mathsrevision.com S4 Credit (b3)5 = b 15 (y9)-5 = y-45 (2m4)2 = 4m8 (10s2)3 = 1000s6 www.mathsrevision.com 1 -3 4m

2 m6 16 5 4 3x 125 27x12 3 Indices www.mathsrevision.com S4 Credit Now try MIA Ex 4.1 & Ex5.1 Ch9 (page 178) 10 Feb 2020 Created by Mr Lafferty Maths Dept Starter Questions www.mathsrevision.com S4 Credit 1.

Calculate 5 + 2 x 3 2. Find the volume of sphere with diameter 50cm. 2 3. Factorise y +5y+6 www.mathsrevision.com Algebraic Operations www.mathsrevision.com S4 Credit Learning Intention Success Criteria 1. To explain how to hand fractional indices of powers. 1. Understand basic rules for fractional indices. 2. Simplify fractional indices. www.mathsrevision.com

Fractions as Indices www.mathsrevision.com S4 Credit 1 2 1 2 1 1 + 2 2 =a a =a a a =a 1 2 a =a www.mathsrevision.com =a Fractions as Indices www.mathsrevision.com S4 Credit

1 3 1 3 1 3 1 1 1 ++ 3 3 3 a a a =a 3 3 1 =a =a 1 3 a a a =a =a 3 1 3

a =a www.mathsrevision.com Fractions as Indices www.mathsrevision.com S4 Credit In general we have 1 n n a = a www.mathsrevision.com Fractions as Indices www.mathsrevision.com S4 Credit Final Rule n m a = a

m n www.mathsrevision.com m n = a Fractions as Indices www.mathsrevision.com S4 Credit Examples : Simplify the following 3 4 a 3 a 2 3 8 3

8 2 2 1 a 1 4 2a 1 3 3 1 4 4 =a a 1 13 2 =4 =a 2 3 =a

www.mathsrevision.com a 2 1 2 a 2 Fractions as Indices www.mathsrevision.com S4 Credit m Examples 3 4 y 3 4 16

a 24 4 8 n n m =a = m an 6 =y =y 3 = 4 3

16 =(2) www.mathsrevision.com =8 Fractions as Indices www.mathsrevision.com S4 Credit m Examples 27 5 3 = 1 27 2 3 4 2a b

5 3 a n = n m =a = m an 1 3 27 5 1 1 = 5 =

3 243 8 12 =2 a b =16a b 4 8 12 www.mathsrevision.com Fractions as Indices www.mathsrevision.com S4 Credit Example : Change to index form 2 5a-3 Example : 1 -4 3 3m 2 2 =

3 2 1 -3 2 5a 2a = 1 52 =1 3 2 5 a2 Change to radical sign 1 3 4 3 =3 m =3 3 3

m www.mathsrevision.com 4 3 =3 4 m Indices www.mathsrevision.com S4 Credit Now try MIA Ex 6.1 Ch9 (page 181) 10 Feb 2020 Created by Mr Lafferty Maths Dept

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