Mathematics for science and technology
Mathematics for science and technology

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Mathematics for science and technology

1.3 Rule 3 – Powers of powers

You know that a2 = a × a.

This can be extended to powers of powers.

So, left parenthesis equation left hand side a cubed times right parenthesis squared super equals right hand side a cubed multiplication a cubed

Using Rule 1 gives:

multiline equation row 1 a cubed multiplication a cubed equals a super open three plus three close row 2 equals a super six

This time the product (3 × 2) of the original powers is the same as the power in result. So, rule 3 can be stated as:

equation left hand side left parenthesis a super m right parenthesis super n equals right hand side a super m times n
Equation label: Rule 3

Again, this rule works for positive and negative indices.

For example, multiline equation row 1 left parenthesis a super negative four right parenthesis cubed equals a super open negative four multiplication three close row 2 equals a super negative 12

So far you have looked at powers that are all integers, however fractional powers are also very common. These will be the subject of the next section.


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