Powers

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

3.5 Powers

How was your weekend?

Planning

• What are powers?
• Vocabulary
• How does an exponent work?
• Negative numbers
  
• Multiplication with powers
• Division with powers

what are powers?

Powers are a shorter way of writing products

Other words for power are index or exponent

Vocabulary

Numbers are in index form if they are written down like 2³

The index form consist of a base number and the power/ index/ exponent

What does the exponent mean?

The power shows how many times a number is multiplied with itself

2×2×2×2=2⁴                               4 times itself
3×3×3×3×3×3×3=3⁷                  7 times itself

2⁴ is read as “two to the forth power” or “two to the power of four”

what is the index form of
5×5×5×5×5×5×5×5

1. 5​7​​
2. 5​8​​
3. 8​5​​
4. 8​7​​

Negative numbers

-3³ = -27                 -1 x (3 x 3 x 3) = -27

(-3)³ = -27              (-3 x -3 x -3)    = -27

Negative numbers

-3² = -9                        -1 x (3 x 3) = -9

(-3)² = 9                       (-3 x -3)     = 9

Combining numbers

Numbers can only be combined if the base numbers are the same!

Combining numbers

Law of multiplication

2⁶ x 2⁴ = 2¹⁰           2⁶⁺⁴

4⁴ x 4² = 4⁶             4⁴⁺²

3⁵ x 3⁷ = 3¹²           3⁵⁺⁷

6⁹

11⁷

6⁷

11⁹

6⁴ x 6³

11⁶ x 11

6² x 6³ x 6⁴

11⁴ x 11⁵

Law of division

Law of division

2⁶ / 2⁴ = 2²          2^6-4

2⁵ / 2² = 2³          2^5-2

3⁵ / 3⁷ = 3^-2        3^5-7

5⁶

5⁵

5²

5³

5⁶ / 5³

5⁶ / 5

5¹¹ / 5⁵

5⁷¹⁴ / 5⁷¹²

power of zero

working on your own

For 5 minutes, work on your own

• 5 minutes silence, no questions
  

• Look back in the presentation
• Start working in Bettermarks (3.5 powers)

After 5 minutes you can work with your neighbour