What are Indices? Indices provide a way of writing numbers in a more convenient form Indices is the plural of Index An Index is often referred to as a.

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Presentation transcript:

What are Indices? Indices provide a way of writing numbers in a more convenient form Indices is the plural of Index An Index is often referred to as a power

For example 5 x 5 x 5 = 53 2 x 2 x 2 x 2 = 24 7 x 7 x 7x 7 x 7 = 75 5 is the INDEX 7 is the BASE NUMBER 75 & 24 are numbers in INDEX FORM

Combining numbers 5 x 5 x 5 x 2 x 2 x 2 x 2 = 53 x 24 We can not write this any more simply Can ONLY do that if BASE NUMBERS are the same

Rule 1 : Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312 General Rule am x an = am+n

Rule 2 : Division 26 ÷ 24 = 22 25 ÷ 22 = 23 35 ÷ 37 = 3-2 General Rule am ÷ an = am-n

Multiplying powers of the same number Copy the text below in to your books and then answer the questions 25 x 22 = 43 x 46 = 62 x 6 = 84 x 83 = 92 x 9 -2 = 2-3 x 2 = 55 x 5 –7 = 3 -2 x 3 = 8 -2 x 8 -3 = Give your answer in power form Example: 55 x 56= 511 When multiplying: Powers of the same base (number) are added. In general: am x an = am+n Base number Power

Answers 25 x 22 = 43 x 46 = 62 x 6 = 84 x 83 = 92 x 9 –2 = 2-3 x 2 = 27 49 63 87 90 = 2 -2 = 5 -2 = 3 -1 = 8 1 =

Dividing powers of the same number Copy the text below in to your books and then answer the questions 25 ÷ 22 = 47 ÷ 45 = 62 ÷ 6 = 84 ÷ 83 = 311 ÷ 35 = 2-3 ÷ 2 = 55 ÷ 5 –7 = 11 -2 ÷ 113 = 7-4 ÷ 7-3 = Give your answer in power form Example: 56 ÷ 52= 54 When dividing: Powers of the same base (number) are subtracted. In general: am ÷ an = am - n Base number Power

Answers 25 ÷ 22 = 47 ÷ 45 = 62 ÷ 6 = 84 ÷ 83 = 311 ÷ 35 = 2-3 ÷ 2 = 25 ÷ 22 = 47 ÷ 45 = 62 ÷ 6 = 84 ÷ 83 = 311 ÷ 35 = 2-3 ÷ 2 = 55 ÷ 5 –7 = 11 -2 ÷ 113 = 7-4 ÷ 7-3 = 23 42 61 = 81 = 36 2 -4 512 11 -5 7-1 =

Rule 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315 General Rule (am)n = am x n

Rule 4 : Index of 0 How could you get an answer of 30? 35 ÷ 35 = 35-5 = 30 30 = 1 General Rule a0 = 1

Putting them together? 26 x 24 23 = 210 23 = 27 35 x 37 34 = 312 34 = 38 25 x 23 24 x 22 = 28 26 = 22

Works with algebra too! a6 x a4 = a10 b5 x b7 = b12 c5 x c3 c4 = c8 c4

8a6 4a4 2 2 ..and a mixture… 2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7