# 5.5.2 Calculator Exploration—Exponents with Negative Numbers

In this exploration, you will explore exponents of negative numbers.

The calculator can be accessed on the left-hand side bar under Toolkit.

Here is an activity to help you understand exponents of negative numbers.

## Activity: Taking Exponents of negative numbers

Copy the table below into your notebook and use the square or button 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 in your math notebook.

### Discussion

Remember to enclose each negative number in parentheses, then follow it by the exponent button (or ^ and the exponent number on your keyboard).

### Answer

The key sequence for finding is

1 | 4 | |||

^{−}1 | ^{−}8 | |||

1 | 16 | |||

^{−}1 | ^{−}32 | |||

1 | 64 |

Look at the table you created in this activity. Can you see a pattern emerging? Was it what you expected to see?

## Activity: Spotting the Pattern

See if you can complete the following sentences:

Raising a negative number to an even exponent gives a ______ number.

Raising a negative number to an odd exponent gives a ______ number.

### Discussion

Remember that an even number divides exactly by 2 (for example, 2, 4, 6 …), while an odd number does not divide exactly by 2 (for example, 1, 3, 5 …).

### Answer

Raising a negative number to an even exponent gives a
*positive* number.

Raising a negative number to an odd exponent gives a
*negative* number.

There are lots of patterns like these in mathematics, and it’s worth watching out for them!

5.5.1 Using the Number Line to Multiply