Index Notation

Index Notation Indices are a form of algebra They are used to help to simplify long expressions. You are probably familiar with ‘squares’ and ‘cubes’ Eg) 5² means ‘5 squared’ (5 x 5) 5³ means ‘5 cubed’ (5 x 5 x 5)

Index Notation Find the value of: a) 3³ = 3 x 3 x 3 = 27 b) 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64 c) 2² + 4³ = (2 x 2) + (4 x 4 x 4) = 4 + 64 = 68

Index Notation Express as a power of a prime number… a) 25 = 5 x 5 = 5² b) 32 = 2 x 2 x 2 x 2 x 2 = 25 c) 81 = 3 x 3 x 3 x 3 = 34

Index Notation Simplify a x a x a x a x a = a5 c x c x c = c3 e x f x e x e x f = e3f2 4 x a x a x 2 x b = 8a2b

Index Notation Simplify: 22 x 23  (2 x 2) x (2 x 2 x 2)  25

Index Notation Simplify: 53 x 54  (5 x 5 x 5) x (5 x 5 x 5 x 5)  57

Index Notation Simplify: a2 x a4  (a x a) x (a x a x a x a)

When multiplying, you add the powers! Index Notation Simplify: ax x ay = ax + y When multiplying, you add the powers!

Index Notation Simplify 24 ÷ 22  2 x 2 x 2 x 2 2 x 2  2 x 2  22

Index Notation Simplify 35 ÷ 3  3 x 3 x 3 x 3 x 3 3  3 x 3 x 3 x 3  34

Index Notation Simplify a6 ÷ a3  a x a x a x a x a x a a x a x a

Index Notation Simplify a4 ÷ a4  a x a x a x a a x a x a x a  a0  1

When dividing, you subtract the powers! Index Notation Simplify ax ÷ ay  ax - y When dividing, you subtract the powers!

Index Notation Simplify 62 x 34 x 63 = 65 x 34

Index Notation Simplify 53 x 56 54 = 55

Index Notation Simplify (23)2 = 23 x 23 = 26

Index Notation Simplify (42)3 = 42 x 42 x 42 = 46

Index Notation Simplify (53)4 = 53 x 53 x 53 x 53 = 512

When you have two powers like this, you multiply them! Index Notation Simplify (xm)n = xmn When you have two powers like this, you multiply them!

Plenary 511 53 58 = 58

Plenary 35 35 35 35 x x x 320

Summary We have learnt what Indices are We have learnt how to work out answers to questions involving Indices We have learnt how to write questions more easily by using Indices