Mathematics for science and technology
Mathematics for science and technology

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Mathematics for science and technology

1.2 Rule 2 – Dividing with powers

This time let’s look at a5 divided by a2, which can be written as:

multiline equation row 1 a super five division a squared equals a multiplication a multiplication a multiplication a multiplication a divided by a multiplication a row 2 equals a multiplication a multiplication a row 3 equals a cubed

This time the difference between the powers (5 and 2) is the same as the power in the final result – giving Rule 2:

equation left hand side a super m division a super n equals right hand side a super open m minus n close
Equation label: (Rule 2)

Thus multiline equation row 1 a super five division a squared equals a super open five minus two close row 2 equals a cubed

Here’s an example with both positive and negative indices.

multiline equation row 1 a squared division a super negative six equals a multiplication a division one divided by a multiplication a multiplication a multiplication a multiplication a multiplication a row 2 equals open a multiplication a close multiplication open a multiplication a multiplication a multiplication a multiplication a multiplication a close row 3 equals a super eight

(Note when you divide by a fraction it is the same as multiplying by the inverted fraction. If you want to revise fractions try another of our badged courses – Succeed with Maths Part 2).

Or using Rule 2:

multiline equation row 1 a squared division a super negative six equals a super open two minus open negative six close close row 2 equals a super eight

It is important to remember that Rules 1 and 2 only work if the powers involve the same base number, for example, you can’t apply them to a3 × b2 or a7 − b5.

There are occasions when you will encounter a power of a power – the next section looks at this situation.

MST_1

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