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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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Tekstslide
Wiskunde
Middelbare school
havo, vwo
Leerjaar 1
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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
=
k
2
+
5
y
=
3
x
4
+
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:
4
3
=
.
.
.
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
4
3
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!
4
c
3
3
d
4
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
=
1
2
f
3
1
2
f
3
m
=
1
2
f
m
=
7
f
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
=
1
2
f
3
1
2
f
3
m
=
1
2
f
m
=
7
f
f
3
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.
c
2
c
6
.
5
c
3
3
c
3
3
c
3
c
3
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!!
c
2
c
6
.
5
c
3
3
c
3
3
c
3
c
3
c
c
2
c
3
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!
2
3
2
4
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:
2
3
2
4
2
7
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.
2
3
2
4
2
7
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:
§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!
Slide 25 - Tekstslide
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