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Every year, without fail, examiners report of too many errors by exam candidates in dealing with indices. This is in part due to weaknesses in working with fractions and negative numbers. But not knowing about the laws of indices and not practising how to apply them contributes to these errors.
Two basic laws of indices
- Multiplication law:
- Division law:
Using these laws - Example 1
- Question
- Answer
Use the multiplication law. This tells you to add the indices.
Example 2
- Question
This could also be written as
- Answer
Use the division law. This tells you to subtract the indices.
Writing this example out in full gives
Example 3
- Question
- Answer
Find the index of the numerator first. Using the multiplication law, this is 7 + 4.
You'll impress the marker in an exam if you write down this intermediate stage! Now use the division law and subtract the indices.
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