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07/04/2019 INDEX NOTATION
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07/04/2019 Guess the Number Pattern : Square Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
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07/04/2019 Guess the Number Pattern : Cube Numbers. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
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07/04/2019 We use index notation to show repeated multiplication by the same number. For example, we can use index notation to write 2 × 2 × 2 × 2 × 2 as index or power 25 base This number is read as ‘two to the power of five’. 25 = 2 × 2 × 2 × 2 × 2 = 32
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07/04/2019 Evaluate the following:
When we raise a negative number to an odd power the answer is negative. 62 = 6 × 6 = 36 34 = 3 × 3 × 3 × 3 = 81 (–5)3 = –5 × –5 × –5 = –125 When we raise a negative number to an even power the answer is positive. 27 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 (–1)5 = –1 × –1 × –1 × –1 × –1 = –1 (–4)4 = –4 × –4 × –4 × –4 = 64
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(23 – 13 + 4 – 8) = (10 + 4 – 8) = (14 – 8) = (6) = 36 07/04/2019
Example (23 – – 8) 2 = ( – 8) 2 = (14 – 8) 2 = (6) 2 = 36
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07/04/2019 Task 1. (38 – 27) 2 1. (3 + 5) 2 110 64 2. (14 - 5) 2 (21 – 18) 3 81 73 3. (6 x 2) - 10 2 2 9 - 5 134 16 4. (2 x 2) 3 64 ( ) - 13 2 60 3 5. (2 + 1) + (2 x 1) 2 17 3 5. (3 x 4) - (3 x 1) 2 117
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MULTIPLICATION AND DIVISION WITH INDICES
07/04/2019 MULTIPLICATION AND DIVISION WITH INDICES
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Multiplying numbers with indices
07/04/2019 Multiplying numbers with indices 34 × 32 = (3 × 3 × 3 × 3) × (3 × 3) = 3 × 3 × 3 × 3 × 3 × 3 = 36 = 3(4 + 2) 73 × 75 = (7 × 7 × 7) × (7 × 7 × 7 × 7 × 7) = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 78 = 7(3 + 5) When we multiply two numbers with the same base, the indices are added. What do you notice? 23 x 25 32 x 35 46 x 44 53 x 51 63 x 63 83 x 89 27 x 22 Try these… 28 37 410 54 66 812 29
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Dividing numbers with indices
07/04/2019 Dividing numbers with indices 4 × 4 × 4 × 4 × 4 4 × 4 = 45 ÷ 42 = 4 × 4 × 4 = 43 = 4(5 – 2) 5 × 5 × 5 × 5 × 5 × 5 5 × 5 × 5 × 5 = 56 ÷ 54 = 5 × 5 = 52 = 5(6 – 4) When we divide two numbers with the same base the indices are subtracted. What do you notice? 27 ÷ 25 312 ÷ 35 49 ÷ 44 53 ÷ 51 623 ÷ 615 83 ÷ 89 21 ÷ 215 Try these… 22 37 45 52 68 8-6 2-14
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07/04/2019 Rules of indices Multiplying When you multiply two things with the same base, just: ADD the powers Leave the base the same Dividing When you divide two things with the same base, just: SUBTRACT the powers
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07/04/2019 Zero indices ANYTHING to the power of 0 is ALWAYS equal to 1 60 = 1 = 1 100 = 1 = 1 x0 = 1 (12y2)0 = 1
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INDICES INCLUDING BRACKETS AND POWERS
07/04/2019 INDICES INCLUDING BRACKETS AND POWERS
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07/04/2019 Brackets with a power
Consider the following: (32)3 = 3 x 3 x 3 x 3 x 3 x 3 = 36 (24)2 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28 (53)3 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 59 When we have brackets with a single term inside and a power outside, the indices are multiplied. What do you notice? (22)3 (32)2 (43)4 (53)2 (6-3)2 (8-2)2 (27)-2 Try these: 26 34 412 56 6-6 8-4 2-14
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07/04/2019 NEGATIVE INDICES
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07/04/2019 Look at the following division: 3 × 3 3 × 3 × 3 × 3 = 1
32 32 ÷ 34 = Using the second index law, 32 ÷ 34 = 3(2 – 4) = 3–2 That means that, Raising a number to the power of –1 is equivalent to finding its reciprocal. 1 32 3–2 = 1 6 1 74 1 53 Similarly, 6–1 = 7–4 = and 5–3 =
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1 1 2-1 means 2 2 1 1 2 2-2 means 4 1 1 3 3-2 means 9 1 1 4 4-3 means
07/04/2019 1 1 - 1 2-1 means 2 2 1 1 - 2 2 2-2 means 4 1 1 - 2 3 3-2 means 9 1 1 - 3 4 4-3 means 64 1 1 a-1 means a - 1 a-2 means a - 2
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07/04/2019
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