Working with powers + scientific notation

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

Math

You need:

Laptop

Notebook

Pencil case

−6​2​​=

1. 12
2. -12
3. 36
4. -36

(−2)​4​​=

Simplify:

6(a+3)=

1. 6a + 9
2. 6a3
3. 6a + 18
4. 18a

Simplify: (type in your answer without spaces)

7(t−5)=

Note: scientific notation

In scientific notation:
189,000,000 =

1. 1.89⋅10​8​​
2. 1.89⋅10​9​​
3. 1.89⋅10​10​​
4. 1.9⋅10​9​​

Write in scientific notation:
78,000
(10 to the power of 5: 10^5 )

Write in normal notation:
(without comma's or points)

5.24⋅10​6​​

t​3​​⋅t​4​​=t⋅t⋅t⋅t⋅t⋅t⋅t=t​7​​

t​5​​ ⋅ t​4​​ = ?

1. 9t
2. t​9​​
3. t​20​​
4. 20t

Powers with a higher exponent

Learning goal:

how to calculate with powers

Recap 

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​​

12f​3​​

m=12f

m=7f

1. *
2. *
3. *
4. *

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=12f​3​​

12f​3​​

m=12f

m=7f

f​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​​

1. &
2. &
3. &
4. &

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 number of 2-s !  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.192 now.

2​3​​

2​4​​

2​7​​

Starter

1. 9p​16​​q​11​​
2. 9p​10​​q​15​​
3. 6p​12​​q​9​​
4. 6p​10​​q​15​​

HOMEWORK:

Homework: 70,71 and 72