1TH/vwo §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.

HV task:

1. Copy the task in your Notebook.

2. Write down a calculation

3. Key in your answer in the next slide.

−(−3)​3​​=

for HV : Copy and make in your Notebook!
=

−(−3)​3​​

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

HV task:        Solution, step by step:

-   -3 x -3 x -3 = 3 x 9 = 27

−(−3)​3​​=

VWO task:   COPY and MAKE in your NOTEBOOK:

This is the Solution:

VWO    TASK 6:

this is a Fotovraag:

MAKE THIS ONE IN YOUR NOTEBOOK: FIRST COPY the TASK!

Then WORK IT OUT, TAKE A PICTURE AND SEND IT IN IN NEXT SLIDE.

TASK 6:

VWO task      EXPLANATION TASK 6:

The exercises above are similar to 45, that you are going to do now. The exercises e t/m h contain more than one

operation.

Work it out completely in your NOTEBOOK!

Not just the answer. Also see next slide!

As you can see, for 45 and 46 the CALCULATIONS are of the greatest importance!

So, when making them, don't just give the answers but show 

all the steps it takes, to get the answer!

HOMEWORK TIME 

H/V:       41 t/m 45

VWO:     42 t/m 46