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

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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

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

11. 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

12. 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

13. 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,…)

14. 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

15. 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!!

16. 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