1. Starter
Estimate the answer to the following:
√27
√105
8.92

2. Index Laws Learning Objectives:
Level 7/Grade B
29/04/2019
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

3. Index Laws How can I simplify: 45 x 43? How can I simplify: 79 x 76?
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

4. 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

5. 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

6. 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

7. 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

8. 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

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

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

11. (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

12. Index Laws Learning Objectives:
Level 8
29/04/2019
Learning Objectives:
Able to multiply terms with the same base
Able to divide terms with the same base
Able to simplify terms with negative
indices

13. Index Laws
Complete the Tarsia puzzle by matching the correct simplified indices to the questions

14. 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

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

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

17. Index Laws Learning Objectives:
Level 8
29/04/2019
Learning Objectives:
Able to multiply and divide terms with the same base
Able to raise a power to another power
Able to simplify terms with negative
indices

18. 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

19. 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 = 1
2-1 = ½
2-2 = ¼
2-3 = ⅛
2-4 =
20 =
2-1 =
2-2 =
2-3 =
2-4 = 1 16

20. 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

21. 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

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. 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

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

25. Some practice… Exercise 10C, page 214 Exercise 10B, page 212 Q1, 2
Q4, 5, 6 (a to c for each)
Q7, 8
Exercise 10B, page 212