1TH/Vwo §7.2 Powers

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

Now comes a powerful paragraph!

§7.2 Powers

Homework:  9  t/m  17

First a task about §7.1

In the next slide send in your

CALCULATION + ANSWER to the task!

NOTE:            this symbol (a point) means 'multiplying'.

So, for example:   

⋅

5⋅6=30

2+6⋅(7+3)=..

2 + 6 x (7 + 3) = ...

2 + 6 x 10 =                      first the addition between the brackets 

2 + 60 =                            then the multiplication

62                                       finally the addition is done

2 + 6 x (7 + 3) = ...

NOT like this however:                       

2 + 6 x 10 =  

60 =                  

2 + 60 =                            

62    ,  because 60  is NOT equal to 62, as is stated here!                                

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- is called:

SQUARING a number.

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

'Square'  is in dutch:      'kwadraat'.

m​2​​

'squaring' in dutch we call this:

'kwadrateren'.  Or:   'het kwadraat nemen van' .

In the next slide

 give the answers to these 5 exercises.

The 5 answers to the SQUARES 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 =            = 81

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

+  Like the word: POWER.

3​4​​

Question:

What is a powerful idea during a long and tiring day?

Solution - see next slide!

A POWERNAP!

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​​

Squaring a number is an example of
raising to a power.

1. true
2. not true

Solution:

Both are examples of raising to a power!

3​4​​=3x3x3x3=81

5​2​​=5x5=25

is the same as .....

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 §7.1!

WHERE DO THE POWERS FIT IN IN THIS LIST?!

THINK ABOUT THIS!

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

So it comes 2nd in place. Brackets go first always!

THINK about this one for a while ... 

You don't have to actually work it out.

Just think about the ORDER in which to work it all out!

Here is the Solution:

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

FOTOVRAAG:

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!  Another common mistake:

                                                        =   36 - 25 = 7 x 11 = 77      because here '7' disappeared for a while!?

7x(6​2​​−2​5​​)

Solution:

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!  Another common mistake:

                                                        =   36 - 25 = 7 x 11 = 77      because here '7' disappeared for a while!?

7x(6​2​​−2​5​​)

As for 16, above, mind 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!

So: show your calculation. It also helps to gain points in the next test!

Homework time.

+  Do §7.2 now.

+   You may skip:   12 and 15 as we have done a lot 

     together!