Mathematics for science and technology
Mathematics for science and technology

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Mathematics for science and technology

1.1 Rule 1 – Multiplying with powers

If you want to multiply a3 by a2 this can be written as:

multiline equation row 1 a cubed multiplication a squared equals open a multiplication a multiplication a close multiplication open a multiplication a close row 2 equals a super five

Comparing the powers shows that the sum of the original powers (3 and 2) equals the power in the answer.

This works with any powers, both positive and negative, where the base number (a) is the same. So, the rule can be generalised as:

equation left hand side a super m multiplication a super n equals right hand side a super open m plus n close
Equation label: (Rule 1)

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

multiline equation row 1 a super negative three multiplication a super five equals one divided by a multiplication a multiplication a multiplication a multiplication a multiplication a multiplication a multiplication a row 2 equals a multiplication a multiplication a multiplication a multiplication a divided by a multiplication a multiplication a row 3 equals a multiplication a row 4 equals a squared

Or using the rule 1:

multiline equation row 1 a super negative three multiplication a super five equals a super open negative three plus five close row 2 equals a squared

This is a much quicker way to the answer.

This idea can be extended to include division, as you will see in the next section.

MST_1

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