1TTO §8.2 Powers

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• Middelbare school
• havo, vwo
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Now comes a powerful paragraph!

§8.2 Powers

When using your calculator:

5 kwadraat kun je op twee manieren doen:

tik 5

tik kwadraat teken 

tik =.

Of: tik 5 en dan 'dakje' [dus ^] en dan 2 en dan =

 

x​2​​

When using your calculator:

 

tik 3

tik dakje [ = ^-knop)

tik 4

en tik dan =

 

3​4​​=

Here is a table with length = 2 m  and also width = 2 m.

The Area (=oppervlakte) = 2 x 2 = 4     

     

Multiplying a number by itself -in this case 2 muliplied by 2- is called:

SQUARING a number.

The result is the SQUARE of a number. Let's look at a few more examples!

m​2​​

Square = vierkant!

Square = vierkant = 'kwadraat' 

3 kwadraat = 

3​2​​=3x3=3kwadraat=9

In the next slide

 give the answers to these 5 exercises.

First copy in your notebook:

1​2​​,2​2​​,3​2​​,4​2​​,5​2​​

The 4 answers to the SQUARES of 1,2,3,4, and 5 are:

1. 1, 2, 3, 4 and 5
2. 1, 4, 9, 16 and 25
3. 2, 4, 6, 8 and 10

Solutions:

So, for example:

the SQUARE of 5 is

5 x 5 = 25.

However ...

sometimes you want to multiply a number by itself more than once. Then we can use a similar Notation as for the Square:

+  For example:  3 x 3 x 3 x 3 = 

+  See the next slide for more! New examples and the new Words that come with this. 

+  Like the word: POWER.

3​4​​

is the same as ........

4​3​​

1. 4 x 4 x 4
2. 4 + 4 +4
3. 4 x 3
4. 64

Explanation:

        means the same as:

4 x 4 x 4, 

but it also means: 64, because that is the outcome.

It doesn't mean 4 + 4 + 4, which you could write as 3 x 4 = 12.

Once more:                      = 4 x 4 x 4 = 64

Remember: a POWER is about multiplying, not adding!

4​3​​

4​3​​

is the same as .....
(more answers possible!)

2​4​​

1. 8
2. 2 x 2 x 2 x 2
3. 16
4. 2 + 2 + 2 + 2

Explanation:

        is the same as:

+   2 x 2 x 2 x 2 , because a power is a multiplication, that is repeated.

+   16, because that's the outcome.

+   however, it's not about adding, so not 2 + 2 + 2 +2.

2​4​​

REMEMBER THIS? IT'S FROM FROM §8.1!

HOWEVER, THE POWERS HAVE TO HAVE A PLACE IN THIS NOW!

SEE NEXT SLIDE.

Watch below: between the 'brackets' and the 'multiplying/dividing' the POWERS are placed!

So it comes 2nd in place.

      Hoe                                                 Haakje    

Moeten                                         Machten

Wij                                                        wortel

Van Deze      vermenigvuldigen  delen

------------>                                                       

Onvoldoendes Afkomen?                               optellen aftrekken

------------------------------>                                                               

THINK about this one for a while ... (You don't have to actually work it out, yet!)

How to work it out and what is the final answer?

Here is the Solution:

(Study it carefully, because you're going to make one yourself!)

H

M

W

VD ->

OA ->

Task:

1. Work this one out on paper.

2. Take a pic and

3. Send it in in next slide!

My work in a Photo:

Solution:

The POWERS between the BRACKETS have to be worked out first!

Following the PRIORITY rules we get:

7 x ( 36 - 32) = 7 x 4 = 28

A common mistake would be: 

7 x ( 12 - 10 ) = 7 x 2 = 14   In this case you've done 6 x 2 and 2 x 5 instead of

calculating POWERS!

Homework time.

+  §8.2 make 11, 14, 15, 16.

As for 18, above, use the remark :

'Calculate as in the example above' !

So don't just give the answers -they are in the Solutionsbook too- but show the process of Calculating!