1. Index Laws Learning Objectives:
Level 7/Grade B
15/05/2019
Learning Objectives:
Able to estimate the answer to a question involving indices
Able to multiply terms with the same base
Able to divide terms with the same base

2. Starter
Starter – no calculators! Write down the first 12 square numbers. Write down the first 6 cube numbers. What is the value of 24?

5. What are the Index Laws? How can I simplify: 45 x 43?
4 x 4 x 4 x 4 x 4 x
4 x 4 x 4
= 48
7 x 7 x 7 x 7 x 7 x 7 x 7 x
7 x 7 x 7 x 7 x 7 x 7
= 715

6. Law 1 : Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312
General Rule:
When multiplying terms with the same base, you add the powers
am x an = am+n
EXAMPLE: 47 x 45 = 47+5 = 412

7. Index Laws How can I simplify 95 ÷ 93? 9 x 9 x 9 x 9 x 9 = 9 x 9 = 92
11 x 11 x 11 x 11 x 11 x 11 x 11
= 115
11 x 11

8. Law 2 : Division 26 ÷ 24 = 22 25 ÷ 22 = 23 35 ÷ 37 = 3-2 General Rule
When dividing terms with the same base, you subtract the powers
am ÷ an = am-n
EXAMPLE: 47 ÷ 45 = 47-5 = 42

9. Index Laws How can I simplify (43)4? How can I simplify (72)5?
4 x 4 x 4 x
4 x 4 x 4 x
4 x 4 x 4 x
4 x 4 x 4
= 412
7 x 7 x
7 x 7 x
7 x 7 x
7 x 7 x
7 x 7
= 710

10. Law 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315
General Rule:
When raising a power to another power, you multiply the powers
(am)n = am x n
EXAMPLE: (47)5= 47 x 5 = 435

11. Index Laws
Simplify the following:
73 x 78 75
𝑥4 x 𝑥9
𝑥5 x 𝑥10

12. Index Laws
Crack the code to reveal an hilarious joke!!

13. Index Laws Learning Objectives:
Level 8
15/05/2019
Learning Objectives:
Able to multiply terms with co-efficients and the same base
Able to divide terms with co-efficients and the same base
Able to simplify terms with negative
indices

14. Starter
89 ÷ 83
(35)8
4𝑥7 x 7𝑥6
(2y3)4

15. Index Laws How can I simplify 5a3 x 6a7? 5 x a x a x a x
6 x a x a x a x a x a x a x a
5 x 6 x a x a x a x a x a x a x a x a x a x a
= 30a10

16. Algebra and Indices
9d6 x 8d3
12e10 x 6e4
24f8 ÷ 6f4
60g12 ÷ 5g3

17. Algebra and Indices (7c3)2 = 7 x c x c x c x 7 x c x c x c
= 7 x 7 x c x c x c x c x c x c
= 49c6
(4j8)3
(5k-3)4
7 x c x c x c
x 7 x c x c x c

18. Law 4: Negative Indices General Rule a-n = 1 an 25 = 32 24 = 16 23 = 8
22 = 4
21 = 2
General Rule
a-n = 1 an
20 =
2-1 =
2-2 =
2-3 =
2-4 =
20 = 1
2-1 = ½
2-2 = ¼
2-3 = ⅛
2-4 =
So basically : Apply the power to the number and flip your answer. EASY!!! 1 16

19. Negative Indices = 1 6 2 = 1 36 = 1 7 3 = 1 343 = 9 x 1 𝑚 4 = 9 𝑚 4=
= 1 36
6-2
7-3
9m-4 = =
= 9 x 1 𝑚 4
= 9 𝑚 4

20. Negative Indices ANSWERS: 1 9 6 b) 1 11 5 c) 1 24 19
d) e) f)
g) 10 𝑔 h) 3 ℎ i) 13 𝑖 10
Simplify:
9 −6 b) 11 −5 c) 24 −19
Solve:
d) −2 e) 2 −4 f) 5 −3
g) 10𝑔 −5 h) 3ℎ −8 i) 13𝑖 −10

21. Law 5: Power 0 25 = 32 24 = 16 23 = 8 22 = 4 GENERAL RULE: 21 = 2
Any term to the power 0 is equal to 1.
20 = 1
2-1 = ½
2-2 = ¼
2-3 = ⅛
2-4 = 1 16

22. Simplify the following, leaving your answers in index notation.
1. (38)4
= 332
2. 7f3 x 9f9
= 63f12
x 1210
= 1214
4. (6m5)3
= 216m15
÷ 2-3
= 28
g7 ÷ 7g2
= 6g5
x 36
x 116
= 310
= 117 35
112 x 113
Solve the following.
= 1 49
= 1 27

23. (a) 32 x 37
(b) 79 x 711
(c) y2 x y5
(d) p5 x p6 x p3
(e) 99 ÷ 92
(f) 417 ÷ 412
(g) h6 ÷ h4
(h) g15 ÷ g12 ÷ g2
(j) 35 ÷ 37
(k) 53 x 5-5
(l) x-3 ÷ x-6
(m) k-7 x k12
(n) a15 x a-2 x a-7
(o) e-3 ÷ e-12 ÷ e6
(p) y5 x y-7 ÷ y3
(q) d-4 ÷ d9 x d-4
(r) (s3)12
(s) (g-2)6
(t) (w5)-3
(u) (b-6)-4
(v) 5t2 x 7t5
(w) 6c5 ÷ 2c3
(x) (9g4)2
(y) (10a2)3

24. More difficult examples46
6p8 x 3p3
9p4 x p7
Simplify:
Solve: 83 85
(4-1)3