1. Index Notation

2. 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)

3. 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) =
= 68

4. 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

5. 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

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

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

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

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

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

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

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

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

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

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

16. Index Notation
Simplify
53 x 56 54
= 55

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

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

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

20. 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!

21. Plenary
511 53 58 = 58

22. Plenary 35 35 35 35 x x x
320

23. 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