Exponent Rules
| 52 |
In the example shown in the box, the 5 is called the base. The 2 is called the exponent or index or power. 5 to the power of 2 = 5 × 5 = 25
| INDEX RULES | |||||||||||
| Rules | Examples | ||||||||||
| Expanding | an = a × a × a × ...... × a | 35 = 3 × 3 × 3 × 3 × 3 = 243 | |||||||||
| Multiplying | ax × ay = a(x+y) | 36 × 32 = 3(6+2) = 38 = 6561 | |||||||||
| Dividing | ax ÷ ay = a(x–y) | 36 ÷ 32 = 3(6–2) = 34 = 81 | |||||||||
| Fractional index | a(1/x) = xth root of a | 9(1/2) = √9 = 3 | |||||||||
| Negative index |
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Example One - Expanding
Expand 53
Answer:
53
= 5 × 5 × 5
= 125
Questions
Expand these.
Q1. 55
Q2. 106
Answers
A1. 3125
A2. 1 000 000
Maths Fun - Body Bacteria
How many bacteria are on your body NOW? Here are some facts to help you work it out...
- There about 5 million bacteria on every centimetre2 of your skin.
- An adult has about 2 metres2 (20 000 centimetres2) of skin.
That probably took a minute for you to work out. How many bacteria are on your skin NOW (a minute later)? Bacteria reproduce by binary fission (splitting in half) every 20 minutes. Therefore, all those bacteria have reproduced (doubled in number) 3 times in the last minute!
Example Two - Multiplying Indices
Calculate 23 × 26. Leave the answer in index form.
Answer:
23 × 26
= 23+6
= 29
Example Three - Multiplying Indices
Calculate 23 × 52 × 24. Leave the answer in index form.
Answer:
23 × 24 × 52
= 23+4 × 52
= 27 × 52
Questions
Multiply these indices. Leave the answer in index form.
Q1. 32 × 35
Q2. 43 × 46
Answers
A1. 37
A2. 49
Example Four - Dividing Indices
Calculate 27 ÷ 24. Leave the answer in index form.
Answer:
27 ÷ 24
| = | 2 × 2 × 2 × 2 × 2 × 2 × 2 |
| 2 × 2 × 2 × 2 |
= 2 × 2 × 2
= 23
Example Five - Dividing Indices
Calculate 105 ÷ 103. Leave the answer in index form.
Answer:
105 ÷ 103
| = | 10 × 10 × 10 × 10 × 10 |
| 10 × 10 × 10 |
= 10 × 10
= 102
Questions
Divide these indices. Leave the answer in index form.
Q1. 36 ÷ 32
Q2. 105 ÷ 102
Answers
A1. 34
A2. 103
Example Six - Fractional Indices
Calculate 1001/2
Answer:
100(1/2)
= √100
= 10
Example Seven - Fractional Indices
Calculate 271/3
Answer:
27(1/3)
= 3√27
= 3
Questions
Calculate these.
Q1. 641/2
Q2. 3431/3
Answers
A1. 8
A2. 7
Example Eight - Negative Indices
Calculate 5 –2
Answer:
5 –2
= 1 ÷ 52
= 1 ÷ 25
= 1⁄25
Example Nine - Negative Indices
Calculate 102 × 10 –4
Answer:
102 × 10 –4
= 102 × (1 ÷ 104)
= 100 ÷ 10000
= 1⁄100
Questions
Calculate these.
Q1. 5 –3
Q2. 4 –3 × 4 –2
Answers
A1. 1⁄125
A2. 1⁄1024
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