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Laws of Indices OCR Module 8
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 = 755 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 24We 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 = 312General Rule am x an = am+n
Rule 2 : Division 26 ÷ 24 = 32 25 ÷ 22 = 23 35 ÷ 37 = 3-2 General Ruleam ÷ an = am-n
Rule 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315General 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
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Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
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