5.5.2 Calculator Exploration—Exponents with Negative Numbers

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

Calculator symbol 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 symbol Activity: Taking Exponents of negative numbers

Copy the table below into your notebook and use the square or x to the y power key 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.

left parenthesis super minus times one right parenthesis squared
left parenthesis super minus times two right parenthesis squared
left parenthesis super minus times one right parenthesis cubed
left parenthesis super minus times two right parenthesis cubed
left parenthesis super minus times one right parenthesis super four
left parenthesis super minus times two right parenthesis super four
left parenthesis super minus times one right parenthesis super five
left parenthesis super minus times two right parenthesis super five
left parenthesis super minus times one right parenthesis super six
left parenthesis super minus times two right parenthesis super six
Hint symbol

Discussion

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

Solution symbol

Answer

The key sequence for finding open negative one close squared is Key sequence showing opening parenthesis plus and minus sign 1 closing parenthesis and x squared

left parenthesis super minus times one right parenthesis squared
1
left parenthesis super minus times two right parenthesis squared
4
left parenthesis super minus times one right parenthesis cubed
1
left parenthesis super minus times two right parenthesis cubed
8
left parenthesis super minus times one right parenthesis super four
1
left parenthesis super minus times two right parenthesis super four
16
left parenthesis super minus times one right parenthesis super five
1
left parenthesis super minus times two right parenthesis super five
32
left parenthesis super minus times one right parenthesis super six
1
left parenthesis super minus times two right parenthesis super six
64

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

Activity symbol 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.

Hint symbol

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 …).

Solution symbol

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

5.5.3 Role of Parentheses