Powers with a higher exponent

§11.6 Powers with a higher exponent

Learning goal:
how to calculate with powers
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Slide 1: Tekstslide
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In deze les zitten 25 slides, met interactieve quizzen en tekstslides.

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§11.6 Powers with a higher exponent

Learning goal:
how to calculate with powers

Slide 1 - Tekstslide

§12.6 powers with a higher exponent 
Introduction:
This paragraph is the follow up of §12.5.
That one was about Quadratic Formulas, so for example:
In §12.6 however, the Exponents are higher, like in:

f=k2+5
y=3x4+4

Slide 2 - Tekstslide

Slide 3 - Tekstslide

Recap from..... §7.2 (!):

Slide 4 - Tekstslide

Slide 5 - Tekstslide

The last 2 slides both were taken from Ch 8!

Question:  Isn't that funny, as we now are doing Ch 12 ?!
Answer:  Not really, because in Maths you often use again
                   what you learned in the past!
                    We're kinda recycling and expanding old knowledge, as it were.
However, the following slides are all about Ch 12.

Slide 6 - Tekstslide

TASK 1:
Work out and answer in the next slide:

43=...

Slide 7 - Tekstslide

Task 1:
4 to the power of 3 equals ...
timer
0:20
A
12
B
64
C
7
D
46

Slide 8 - Quizvraag

Solution:
                  = 4 x 4 x 4 = 64
43

Slide 9 - Tekstslide

As I said in earlier lessons:
+ adding terms is only possible if there are Like Terms,
    for example:    7z + 5z = 12z,  but
+ multiplying is always possible, for example:
    h = 4 x c x c x c =                          g = 0.5 x d x d x d x d x 6 = 
As you see: multiply the numbers and multiply the letters!
4c3
3d4

Slide 10 - Tekstslide

Slide 11 - Tekstslide

Task 2:
Write as third power:
m = 4 x f x f x f x 3    Choose the good answer from:
A.                                     B.                                     C.                                    D.  

Remember your answer and answer in the next slide.
m=12f3
12f3
m=12f
m=7f
timer
0:25

Slide 12 - Tekstslide


A
*
B
*
C
*
D
*

Slide 13 - Quizvraag

Solution:
Shorten:
m = 4 x f x f x f x 3    Choose the good answer from:
A.                                     B.                                     C.                                    D.  
 
As       4 x3 = 12      and    f x f x f =                      C. is the good answer!
m=12f3
12f3
m=12f
m=7f
f3

Slide 14 - Tekstslide

Task 3:
Write as a third power and answer in the next slide:
d =  6 x         x         x 0.5 = ...  
A.  d =                                                       C.  d = 
B.   d =                                                      D.     
c2
c
6.5c3
3c3
3c
3c3
timer
0:21

Slide 15 - Tekstslide


A
&
B
&
C
&
D
&

Slide 16 - Quizvraag

Solution:
Write as a third power and answer in the next slide:
d =  6 x         x         x 0.5 = ...  
A.  d =                                                       C.  d = 
B.   d =                                                      D.  
Because 6 x 0.5 = 3   and             x             =                 ,            So   C. is correct!!
c2
c
6.5c3
3c3
3c
3c3
c
c2
c3

Slide 17 - Tekstslide

Slide 18 - Tekstslide

Something new now:
How to write this as one power:
x                  =   .......
????????????
Watch the next slide for a simple way to do this!

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Slide 19 - Tekstslide

How to write this as one power?
First we write it as long as possible:
             x                  =   2 x 2 x 2     x   2 x 2 x 2 x 2      
This last expression, with only multiplications of 2, we can write as ONE POWER, by just counting the number of 2-s !  Then we get:





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Slide 20 - Tekstslide

summarizing:

             x                  =   2 x 2 x 2     x   2 x 2 x 2 x 2      =   
Wait a sec: What we actually did was ADDING the EXPONENTS
together. In this way we got the NEW EXPONENT!
Let's study the THEORY from p.192 now.





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Slide 21 - Tekstslide

Slide 22 - Tekstslide

Slide 23 - Tekstslide

This was a lot of new stuff!
However now you're going through the paragraph in your own tempo and then all will become more clear.
If not yet.

Slide 24 - Tekstslide

HOMEWORK:
60,63 and 65 for Monday!

Slide 25 - Tekstslide