1. Working with Powers Definition of Powers Integer Exponents
The seven Exponent Rules

2. Repeated multiplications…
2 × 2 =
2 × 2 × 2 =
2 × 2 × 2 × 2 =
How can we write these in shorter notation?

3. For repeated addition we use multiplication
For repeated multiplication we use exponents
= 5 × 3
3 × 3 × 3 × 3 × 3 =

4. Write these numbers using exponential notation:
= 10?
27 = 3?
32 = 2?
104 33 25

5. Computer Memory
A byte is capable of storing one letter of the alphabet. For example, the word “math” requires four bytes to store in a computer. Bytes of computer memory are often manufactured in amounts equal to powers of 2.

6. For Example 1 kilobyte (1Kb) = 210 = 1 megabyte (1 Mb) = 220 =
(about a thousand bytes)
1 megabyte (1 Mb) = 220 =
(about a thousand kilobytes)
1 gigabyte (1 Gb) = 230 =
(about a thousand megabytes)
1024

7. Integer Exponents 43 is called a power 43 = 4 x 4 x 4 = 64
Base 4
Exponent 3
43 is called a power
43 = 4 x 4 x 4
= 64
You need to know what is meant by base, exponent and power.

8. You try these . . . 72 54 43
= 49
= 625
= 64

9. Exponent Rules 1. 2. 3. 4. 5. 6. 7.
These rules will be explained in the following slides

10. Exponent Rule #1 #1 n times 5 times Why put a 1 at the beginning?
That’s why!

11. Exponent Rule #2 #2
Any power with an exponent of 0 is equal to 1

12. a0 = 1 40 90
170 =1 M0
(pq)0
(2x2y)0 =1 =1 =1 =1 =1

13. Exponent Rule #3 #3
n times
4 times
A negative exponents means divide

14. Negative Exponents
3-1
7-1
5-2
2-4
(1/2) -1
(3/4) -2

15. M-2
x-5
= y3

16. Operations with Exponents
Multiply: (x3)∙(x4)
A5 ∙ A4 =
Divide:
= (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x)
= (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x)
= x7 A9
= m2

17. Multiplying Exponents
aman=?

18. Exponent Rule #4 #4
When multiplying powers with the same base, add the exponents.

19. x5x4 y-2y7 b3b-6 m6m-6 (2x5)(4x-3) 2z-1z5w-6w-2 = x9 = y5 = b-3 = m0
= 2w-8z4

20. Dividing Exponents

21. Exponent Rule #5 #5
When dividing powers with the same base, subtract the exponents.

22. = x4
= y5

23. Powering Exponents
(am)n=?

24. Exponent Rule #6 #6
When taking a powers of a power (one base only), multiply the exponents.

25. (w4)5
(p-3)4
(5x4)-2
(-3y-7)3
= w20
= p-12
= 5-2x-8
= -33y-21

26. Powering Exponents

27. Exponent Rule #7 #7 Powers of products or quotients
When taking a powers of a product or quotient, distribute the exponent into the bracket.

29. Exponent Rules 1. 2. 3. 4. 5. 6. 7.