Succeed with maths – Part 1

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

# 2 Calculator exploration: exponents with negative numbers

From your previous study you know that when a number is raised to a certain whole number, exponent or power, that is an instruction to multiply the number by itself as many times as the value of the power. So, 33 = 3 × 3 × 3. In this activity you’re going to explore what happens when the number to be raised to a certain power is negative.

## Activity 6 Taking exponents of negative numbers

Timing: Allow approximately 10 minutes

Copy the table below onto a piece of paper and use the exponent button on your calculator to find the value of each of the following. Before you start, think about what pattern you might see and make a note of it.

### Table 4 Exponents

 (–1)2 _ (–2)2 _ (–1)3 _ (–2)3 _ (–1)4 _ (–2)4 _ (–1)5 _ (–2)5 _ (–1)6 _ (–2)6 _

#### Table 4 Exponents (completed)

 (–1)2 1 (–2)2 4 (–1)3 –1 (–2)3 –8 (–1)4 1 (–2)4 16 (–1)5 –1 (–2)5 –32 (–1)6 1 (–2)6 64

The following patterns should be quite clear in the table:

• raising a negative number to an even exponent gives a positive number
• raising a negative number to an odd exponent gives a negative number.

Looking at what is happening, it should be clear that this was the answer to expect:

• (–2)4 = (–2) × (–2) × (–2) × (–2) = 4 × 4 = 16 (since negative × negative = positive)
• (–2)3 = (–2) × (–2) × (–2) = 4 × (–2) = –8 (since negative × negative = positive, and positive × negative = negative).

There are lots of patterns like these in mathematics. It’s worth watching out for them, as they often give shortcuts to an answer by enabling rules to be written and mathematical theories to be developed that can be used with any appropriate situation.

The next section is one final recap of all the rules that you have learned involving negative numbers.

Skip Your course resources
SWMB_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