Level 7Grade B Index Laws 08032021 Learning Objectives

Level 7/Grade B Index Laws 08/03/2021 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 – 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 = 48 • How can I simplify: 79 x 76? 7 x 7 x 7 x 7 = 715

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

Index Laws • How can I simplify 95 ÷ 93? 9 x 9 x 9 = 9 x 9 = 92 • How can I simplify 117 ÷ 112? 11 x 11 x 11 = 115

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

Index Laws • 4 3 How can I simplify (4 ) ? 4 x 4 x 4 x 4 = 412 • 5 2 How can I simplify (7 ) ? 7 x 7 x 7 x 7 = 710

Law 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 = 315 General Rule: When raising a power to another power, you multiply the powers (am)n = am x n 5 7 EXAMPLE: (4 ) = 47 x 5 = 435

Index Laws • Simplify the following: 73 x 78 75

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

Level 8 Index Laws 08/03/2021 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 •

Index Laws • How can I simplify 5 a 3 x 6 a 7? 5 x a x a x 6 x a x a 5 x 6 x a x a x a = 30 a 10

Algebra and Indices • 9 d 6 x 8 d 3 • 12 e 10 x 6 e 4 • 24 f 8 ÷ 6 f 4 • 60 g 12 ÷ 5 g 3

Algebra and Indices • 2 3 (7 c ) = • 3 8 (4 j ) • 4 -3 (5 k ) 7 x c x c x 7 x c x c = 7 x c x c = 49 c 6

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

Negative Indices • 6 -2 • 7 -3 • 9 m-4

Negative Indices •

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

Simplify the following, leaving your answers in index notation. 4 8 1. (3 ) 2. 7 f 3 x 9 f 9 = 63 f 12 3. 124 x 1210 = 1214 3 5 4. (6 m ) = 216 m 15 5. 25 ÷ 2 -3 = 28 6. 42 g 7 ÷ 7 g 2 = 6 g 5 7. 39 x 36 = 310 35 Solve the following. 8. 116 x 116 112 x 113 9. 7 -2 = 332 10. 3 -3 = 117

(a) 32 x 37 (b) 79 x 711 (c) y 2 x y 5 (d) p 5 x p 6 x p 3 (e) 99 ÷ 92 (f) 417 ÷ 412 (g) h 6 ÷ h 4 (h) g 15 ÷ g 12 ÷ g 2 (j) 35 ÷ 37 (k) 53 x 5 -5 (l) x-3 ÷ x-6 (m) k-7 x k 12 (p) y 5 x y-7 ÷ y 3 (q) d-4 ÷ d 9 x d-4 (n) a 15 x a-2 x a-7 (o) e-3 ÷ e-12 ÷ e 6 (r) (s 3)12 (s) (g-2)6 (t) (w 5)-3 (u) (b-6)-4 (v) 5 t 2 x 7 t 5 (w) 6 c 5 ÷ 2 c 3 (x) (9 g 4)2 (y) (10 a 2)3

More difficult examples 43 x 47 46 • Simplify: • Solve: 83 85 6 p 8 x 3 p 3 9 p 4 x p 7 3 -1 (4 )