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# What is an index law?

By Filsan on the 6th of December, 2012

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What is an index law?

Some numbers can be written in mathematical shorthand
if the number is the product of "repeating numbers".
eg  100 is the product of 10 multiplying itself two times:
100 = 10 x 10
or
64 is the product of 2 multiplying itself six times.
64 = 2 x 2 x 2 x 2 x 2 x 2

These numbers can be written in shorthand.

and

Index Law 1:

Index Law 2:

Index Law 3:

Index Law 4:

Index Law 5:

Index Law 6:

By Bridget Gaskin on the 17th of January, 2013

## Use index laws to evaluate any expression involving powers

Index form is another way of writing numbers, which sometimes looks neater, or simpler.

49 can be written as 7 for example, or 175,616 can be written as 563.

A number with a large index, such as 524, is a very big number.  If we ever had to multiply something like 524 x 520, it would take a long time, look messy, and involve having to write out number with dozens of digits.

Luckily, we have discovered special rules which can make the calculation much easier.  Provided the base number is the same, we can just add the indices together

e.g. 524 x 520 = 524+20 = 544

This doesn’t work if the base numbers are different

e.g. 524 x 720 is NOT 544, or 3544, or 1244

In algebra, we can do the same thing, provided the letter is the same:

e.g. y15 x y10 = y15+10 = y25

If we are dividing numbers in index form, we can subtract the indices.

e.g. y15 ÷ y10 = y15-10 = y5

## Follow the links below to see how this topic has appeared in past exam papers

AQA Unit 2 March 2011 (H) - Page 8, Question 12(b)

Other Relates Topics…

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