1Tvwo §11.6 Powers with a higher exponent

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• Middelbare school
• havo, vwo
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§11.6 Powers with a higher exponent

However first:

Refresh a little

It is not as bad as this. 

It's just good old fashioned

 MATHS!

§11.6 powers with a higher exponent 

Introduction:

This paragraph is the follow up of §11.5.

That one was about Quadratic Formulas, so for example:

In §11.6 however, the Exponents are higher, like in:

f=k​2​​+5

y=3x​4​​+4

Recap from..... §7.2 (!):

The last 2 slides both were taken from Ch 8!

Question:  Isn't that funny, as we now are doing Ch 11 ?!

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 11.

TASK 1:

Work out and answer in the next slide:

4​3​​=...

Task 1:
4 to the power of 3 equals ...

1. 12
2. 64
3. 7
4. 46

Solution:

                  = 4 x 4 x 4 = 64

4​3​​

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!

4c​3​​

3d​4​​

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=12f​3​​

m=12f

m=7f

7f​3​​

m = 4 x f x f x f x 3

1. 7f
2. 12f
3. 12f​3​​
4. 7f​3​​

Solution:

Shorten:

m = 4 x f x f x f x 3    Choose the good answer from:

A.                                     B.                                     C.                                    D.  m = 

 

As       4 x3 = 12      and    f x f x f =                      C. is the good answer!

m=12f​3​​

m=12f

m=7f

f​3​​

7f​3​​

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

6.5c​3​​

3c​3​​

3c

3c​3​​

d=

c​2​​

6⋅c⋅c​2​​⋅0.5

1. d=6.5c​3​​
2. d=3c​​​
3. d=3c​3​​
4. 3c​3​​

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

6.5c​3​​

3c​3​​

3c

3c​3​​

c

c​2​​

c​3​​

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​​

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 numbers above the 2 !  Then we get:

2​3​​

2​4​​

2​7​​

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.195 now.

2​3​​

2​4​​

2​7​​

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.

HOMEWORK:

§11.6 Choose your learning path

Check your answers with the solutions book in Teams!