Index form is another way of writing numbers, which sometimes looks neater, or simpler. 49 can be written as 72, 9 can be written as 32 and finally 200 can be written as 23 x 52 (8 x 25).

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. 51/3 x 51/3 = 51/3+1/3 = 52/3

This doesn’t work if the base numbers are different

e.g. 51/3 x 71/3 is NOT 52/3, or 352/3, or 122/3

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

e.g. y2/7 x y3/7 = y2/7+3/7 = y5/7

e.g. s-2 x s5 = s-2+5 = s3

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

e.g. y2/7 ÷ y3/7 = y2/7-3/7 = y-1/7

e.g. s-2 ÷ s5 = s-2-5 = s-7

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