Succeed with maths – Part 2
Succeed with maths – Part 2

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

Succeed with maths – Part 2

2.4 Negative exponents

The same approach used to understand what zero as a power means can also be used for negative exponents or powers.

This time showing 10 squared division 10 super six as a fraction, simplifying and using the rules for powers with the same base. This gives:

equation sequence 10 squared division 10 super six equals 10 squared divided by 10 super six equals 10 multiplication 10 divided by 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals one divided by 10 multiplication 10 multiplication 10 multiplication 10 equals one divided by 10 super four

So,

equation left hand side 10 squared division 10 super six equals right hand side one divided by 10 super four

Now, using the rule for dividing numbers with the same base:

equation sequence 10 squared division 10 super six equals 10 super open two minus six close equals 10 super negative four

Putting these two results together gives:

equation left hand side 10 super negative four equals right hand side one divided by 10 super four

In the same way, five super negative two means one divided by five squared, or one divided by five multiplication five, which is equivalent to one divided by 25.

Since five squared is 25 and five super negative two is one divided by 25, in maths 5-2 is said to be the reciprocal of 52. So, negative powers represent the reciprocal of the same positive power.

Negative powers of ten then enable small numbers to be shown using scientific notation. Before that though you will practise understanding and writing negative powers in the next activity.

Activity _unit6.2.4 Activity 5 Understanding and writing negative powers

Timing: Allow approximately 10 minutes

Without using your calculator, write the following numbers as fractions or whole numbers, as appropriate.

Remember you can always click on ‘reveal comment’ for a hint if you get stuck.

  • a.two super negative three

Answer

  • a.equation sequence two super negative three equals one divided by two cubed equals one divided by two multiplication two multiplication two equals one divided by eight
  • b.three super negative four

Answer

  • b.equation sequence three super negative four equals one divided by three super four equals one divided by three multiplication three multiplication three multiplication three equals one divided by 81
  • c.10 super negative six

Answer

  • c.equation sequence 10 super negative six equals one divided by 10 super six equals one divided by 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals one divided by one 000 000

Write the following as powers of ten.

  • d.0.01

Discussion

Convert the number to a fraction first, think about place value if you need to.

Answer

  • d.equation sequence 0.01 equals one divided by 100 equals one divided by 10 squared equals 10 super negative two
  • e.0.00001

Answer

  • e.equation sequence 0.00001 equals one divided by 100000 equals one divided by 10 super five equals 10 super negative five
Skip Your course resources
SWMB_2

Take your learning further371

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 courses372.

If you are new to university level study, we offer two introductory routes to our qualifications. Find out Where to take your learning next?373 You could either choose to start with an Access courses374or an open box module, which allows you to count your previous learning towards an Open University qualification.

Not ready for University study then browse over 1000 free courses on OpenLearn375 and sign up to our newsletter376 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