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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Negative Indices ANSWERS: 1 9 6 b) 1 11 5 c) 1 24 19 d) 1 64 e) 1 16 f) 1 125 g) 10 𝑔 5 h) 3 ℎ 8 i) 13 𝑖 10 Simplify: 9 −6 b) 11 −5 c) 24 −19 Solve: d) 8 −2 e) 2 −4 f) 5 −3 g) 10𝑔 −5 h) 3ℎ −8 i) 13𝑖 −10

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

Simplify the following, leaving your answers in index notation. 1. (38)4 = 332 2. 7f3 x 9f9 = 63f12 3. 124 x 1210 = 1214 4. (6m5)3 = 216m15 5. 25 ÷ 2-3 = 28 6. 42g7 ÷ 7g2 = 6g5 7. 39 x 36 8. 116 x 116 = 310 = 117 35 112 x 113 Solve the following. = 1 49 = 1 27 9. 7-2 10. 3-3

(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

More difficult examples 46 6p8 x 3p3 9p4 x p7 Simplify: Solve: 83 85 (4-1)3