# 1TH/vwo §11.6 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: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 1

This lesson contains 25 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

## Items in this lesson

§11.6 Powers with a higher exponent

Learning goal:
how to calculate with powers

#### Slide 1 -Slide

§12.6 powers with a higher exponent
Introduction:
This paragraph is the follow up of §12.5.
In §12.6 however, the Exponents are higher, like in:

f=k2+5
y=3x4+4

#### Slide 3 -Slide

Recap from..... §7.2 (!):

#### Slide 5 -Slide

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 -Slide

Work out and answer in the next slide:

43=...

#### Slide 7 -Slide

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

#### Slide 8 -Quiz

Solution:
= 4 x 4 x 4 = 64
43

#### Slide 9 -Slide

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 11 -Slide

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

m=12f3
12f3
m=12f
m=7f
timer
0:25

A
*
B
*
C
*
D
*

#### Slide 13 -Quiz

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 -Slide

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

A
&
B
&
C
&
D
&

#### Slide 16 -Quiz

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 18 -Slide

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

23
24

#### Slide 19 -Slide

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:

23
24
27

#### Slide 20 -Slide

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.

23
24
27

#### Slide 23 -Slide

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 -Slide

HOMEWORK:
§11.6
Havo and H/V:   Skip: 41, 42, 43.   Do:  S44, 45, S46, 47, 49, S50, 51
VWO:    Skip: 41 t/m 44     Do: 45, 46, 47, 49, 51,   C11 and C12
Good luck!