Mathematics for science and technology
Mathematics for science and technology

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

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.

MST_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371