Laws of indices
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Indices provide a way to write numbers in a more compact form. An index is often called a power. Some key rules for working with indices include: 1. Multiplication: When multiplying the same base number, add the indices (e.g. a3 × a4 = a3+4 = a7). 2. Division: When dividing the same base number, subtract the indices (e.g. a5 ÷ a3 = a5-3 = a2). 3. Brackets: The index is applied to the entire bracketed term (e.g. (a3)4 = a3 × 4 = a12). These rules allow complex expressions to
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Laws of indices
- 1. Laws of Indices OCR Module 8
- 2. 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
- 3. 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 7 is the BASE NUMBER 5 is the INDEX 75 & 24 are numbers in INDEX FORM
- 4. 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
- 5. Rule 1 : Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312 General Rule am x an = am+n
- 6. Rule 2 : Division 26 ÷ 24 = 32 25 ÷ 22 = 23 35 ÷ 37 = 3-2 General Rule am ÷ an = am-n
- 7. Rule 3 : Brackets (26 )2 = 26 x 26 = 212 (35 )3 = 35 x 35 x 35 = 315 General Rule (am )n = am x n
- 8. Rule 4 : Index of 0 How could you get an answer of 30 ? 35 ÷ 35 = 35-5 = 30 30 = 1 General Rule a0 = 1
- 9. Putting them together? 26 x 24 23 = 210 23 35 x 37 34 = 312 34 = 27 = 38 25 x 23 24 x 22 = 28 26 = 22
- 10. Works with algebra too! a6 x a4 = a10 b5 x b7 = b12 a5 x a3 a4 x a6 = a8 a10 = a-2 c5 x c3 c4 = c8 c4 = c4
- 11. ..and a mixture… 2a3 x 3a4 = 6a7 = 2 x 3 x a3 x a4 8a6 ÷ 4a4 = 2a2 = (8 ÷ 4) x (a6 ÷ a4 ) 8a6 4a4 2 2