Calculations in standard index form

Multiplying and dividing numbers in standard form

Here you can use the rules for multiplying and dividing powers. Remember these rules:

• To multiply powers you add, eg
• To divide powers you subtract, eg

Simplify .

Solution

It is useful to separate the numbers and the indices, and then multiply the by and add the powers of :

A similar method is used when dividing:

Simplify .

Solution

Another way to write a division is to write it in the form of a fraction. The numbers and the indices can then be separated, before dividing the by and subtracting the powers of :

.

Question

Simplify .

Did you get ?

Remember to write the division in the form of a fraction to start.

Remember you should first work out , then subtract the powers of (because it is division), like this:

.

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