Discover the 1st Law of Indices 45 x 43 = 48 76 x 77 = 713 35 x 3-7 = 3-2 What do you notice?

Discover the 2nd Law of Indices 95 ÷ 92 = 93 46 ÷ 44 = 42 35 ÷ 3-7 = 312 What do you notice?

Law 1: Multiplying Indices Simplify the following leaving in index form. 83 × 84 = 83 84 8×8×8 × 8×8×8×8 = 87 What’s the shortcut? 83 × 84 = 3 4 8 = 87 + Remember this only works for numbers with the SAME BASE number

Law 1: Multiplying Indices Simplify the following leaving in index form. 52 × 54 = 52 54 5×5 × 5×5×5×5 = 56 What’s the shortcut? 52 × 54 = 2 4 5 = 56 + Remember this only works for numbers with the SAME BASE number

Law 1: Multiplying Indices Simplify the following leaving in index form. a3 × a4 = a3 a4 a × a × a × a × a × a × a = a7 What’s the shortcut? a3 × a4 = 3 4 a = a7 + Remember this only works for numbers with the SAME BASE letter

Am I Correct? 56 x 65 = 3011 56 x 55 = 530 56 x 55 = 511 THUMBS UP IF CORRECT THUMBS DOWN IF NOT – ASK SOMEONE TO EXPLAIN WHY

Remember this only works for numbers with the Law 2: Dividing Indices Simplify the following leaving in index form. 25 ÷ 22= 25 22 2 x 25 22 = 2 x = 23 What’s the shortcut? 25 ÷ 22 = 5 2 2 - = 23 Remember this only works for numbers with the SAME BASE number

Remember this only works for numbers with the Law 2: Dividing Indices Simplify the following leaving in index form. 46 ÷ 44= 4 x x 4 46 44 46 44 = 4 x 4 x x = 42 What’s the shortcut? 46 ÷ 44 = 6 4 4 - = 42 Remember this only works for numbers with the SAME BASE number

Remember this only works for numbers with the Law 2: Dividing Indices Simplify the following leaving in index form. b3 ÷ b2= b x b3 b2 b3 b2 = b x = b1 = b What’s the shortcut? b3 ÷ b2 = 3 2 b - = b1 = b Remember this only works for numbers with the SAME BASE letter

Am I Correct? 212 ÷ 23 = 24 212 ÷ 23 = 29 2412 ÷ 23 = 124 THUMBS UP IF CORRECT THUMBS DOWN IF NOT – ASK SOMEONE TO EXPLAIN WHY

To be able to make use of the first two laws of indices By the end of the lesson, we will be able to: understand that to multiply numbers in index form with the same base, we add the powers understand that to divide numbers in index form with the same base, we subtract the powers understand that these laws of indices only apply when the base of the numbers is the same

Questions: Using SHORTCUT Simplify the following numbers, leaving your answers in index form: 1. (a) 23 x 22 (b) 35 x 32 (c) 73 x 7 (d) 95 x 92 25 37 74 97 2. (a) 23 ÷ 22 (b) 35 ÷ 32 (c) 73 ÷ 7 (d) 95 ÷ 92 2 33 72 93

MISTAKE MINIONS Question: Simplify n3 x n5 Answer: 3 x 5 = 15 Give Minion Dave a TOP TIP to help him improve his understanding on multiplying indices! Answer: 3 x 5 = 15 n3 x n5 = n15 On your mini-whiteboards – write the tip! And work it out correctly (ask a student to come out next to you to explain – Dear Dave,…)

MISTAKE MINIONS Question: Simplify w8 ÷ w4 Answer: 8 ÷ 4 = 2 Give Minion Kevin a TOP TIP to help him improve his understanding on dividing indices! Answer: 8 ÷ 4 = 2 w8 ÷ w4 = w2

MISTAKE MINIONS Question: Simplify 56 ÷ 62 Give Minion Stuart a TOP TIP to help him improve his understanding on the Laws of indices! Answer: 6 - 2 = 4 56 ÷ 62 = 54 We do not have a law about this!!

Homework for Tomorrow STP 8 Pg 22-23 Exercise 1b Nos. 1-10 Index Law 1: Multiplying Indices (ADD POWERS) Exercise 1b Nos. 1-10 Index Law 2: Dividing Indices (SUBTRACT POWERS) Exercise 1c Nos. 1-10