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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 = 75
7 is the BASE NUMBER
5 is the INDEX
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
= 32
25 ÷ 22
= 23
35 ÷ 37
= 3-2
General Rule
am ÷ an = am-n
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
35 x 37
34
= 312
34
= 27
= 38
25 x 23
24 x 22
= 28
26
= 22
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
..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

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laws_of_indices.pptx

  • 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