1Tvwo §8.5 Powers of negative numbers

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

To understand §8.5 better, we first shortly look back at 

POWERS.

Because .... what are powers again?!

Powers were explained earlier this year, in §7.2

Let's repeat that explanation first!

5​3​​=....

1. 125
2. 15
3. 625

Task 1:

Key in your answer in the next slide!

Who's right about: the square of -3 ?
Paulo says: 9
Sabine says: -9

1. Sabine
2. both
3. Paulo
4. neither

explanation:

Task 2:

-           = 25      A

-           = - 25   B

-           = 10       C

-           = - 10    D    Fill in the good answer in the next slide.

5​2​​

5​2​​

5​2​​

5​2​​

= ...

−5​2​​

1. 25
2. - 25
3. 10
4. - 10

explanation:

-         =    -  5 x 5 = - 25

So the key to the answer is that only 5 is squared, but not

the minus sign!!

Next is the ORDER of OPERATIONS (volgorde van bewerkingen).

5​2​​

After this short REFRESH, we are in §8.5 now.

Think of a good answer.

No calculation needed this time!

Do you know what power is?

Watch the next slide!

After all this squaring ......

+ we'll deal with higher powers too!

What does this mean:                  ?

it means                 4 x 4 x 4

So                             4 x 4 x 4 = 64

4​3​​

4​3​​=

Task : 

in the same way do:

=  ............

Key in your answer in the next slide.

(−4)​3​​

Task :

(−4)​3​​

1. 64
2. -64
3. -12
4. 12

Explanation Task :

=  -4 x -4 x -4 = -64

(−4)​3​​

Further Explanation Task : 

=   -   4 x 4 x 4 = -64

                        = -4 x -4 x -4 = -64                       

So, do             and                    give the same outcome?!

Indeed, they do!!        

−4​3​​

(−4)​3​​

−4​3​​

(−4)​3​​

What are the two answers?

1. 125 and 625
2. 125 and -625
3. -125 and 625
4. -125 and -625

Let's study a few more difficult tasks together.

For this it is important to work it out on paper,

just like on a test!

Open your NOTEBOOK en

GET a PEN, please.

task:

1. Copy the task in your Notebook.

2. Write down a calculation

3. Key in your answer in the next slide.

−(−3)​3​​=

Copy and work out in your Notebook!
=

−(−3)​3​​

1. -9
2. 27
3. -27
4. -6

Solution, step by step:

     -  [-3  x  -3  x  -3] = - - 27 = 27

−(−3)​3​​=

task:   work it out in your NOTEBOOK:

This is the Solution:

TASK:

this is a Fotovraag:

WORK THIS ONE OUT IN YOUR NOTEBOOK: FIRST COPY the TASK!

THEN TAKE A PICTURE AND SEND IT IN, IN THE NEXT SLIDE.

TASK:

EXPLANATION TASK:

The exercises above are similar to 45. 

The exercises e t/m h contain more than one operation.

Work it out completely in your NOTEBOOK!

Not just the answer.

HOMEWORK TIME 

 §8.5 Powers of negative numbers: Do the Challenge Path

Check your answers with the solutionsbook in Teams.