1. DAILY WARMUP
1. (-12)² = 2. -4³ = 3. What is the base? 36⁸ 4. What is the exponent? 72⁸ 5. (3 + 7)³ =
144
-64 36 8
1000

2. Exponents
An exponent tells how many times a number is multiplied by itself.
Base ⁵
Exponent

3. Expanded Form
Expanded Form – A number is written in expanded form when the base is multiplied the number of times indicated by the exponent. Write 86 in expanded form. 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 You try it! Write (-2)5 in expanded form. -2 ∙ -2 ∙ -2 ∙ -2 ∙ -2

4. Exponential Form
Exponential Form – a number is in exponential form when it is written with a base and an exponent. Write 9 ∙ 9 ∙ 9 ∙ 9 in exponential form. 9⁴ Write 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 in exponential form. 7⁶

5. X0 = 1 990= 1 Examples: 20=1 Zero Rule
Any non-zero number raised to the
zero power equals one
X0 = 1
Examples: 20=1
990= 1
That seems wrong!
Anything to the zero power is equal to 1 !?!?
…Well click on the information button for an explanation!

6. Any number raised to the power of one equals itself.
Rule of One
Any number raised to the power of one equals itself.
x1=x
Examples: 171 = 17
991 = 99
Well this one is easy!

7. Multiplying Exponents

8. What does this expression really mean?
53 ∙ 54

9. What does this expression really mean?
53 ∙ 54
5 ∙ 5 ∙ 5

10. What does this expression really mean?
53 ∙ 54
5 ∙ 5 ∙ ∙ 5 ∙ 5 ∙ 5

11. What does this expression really mean?
53 ∙ 54
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

12. What does this expression really mean?
53 ∙ 54
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 = 57

13. What does this expression really mean?
53 ∙ 54
= 57
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 = 57

14. Let’s look at another example.
35 ∙ 34

15. Let’s look at another example.
35 ∙ 34
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

16. Let’s look at another example.
35 ∙ 34
3 ∙ 3 ∙ 3 ∙ 3 ∙ ∙ 3 ∙ 3 ∙ 3

17. Let’s look at another example.
35 ∙ 34
= 39 39
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 =

18. From these 2 examples, we can draw a conclusion.
3 + 4 = 7
53 ∙ 54
= 57
When multiplying with two bases that are the same, keep the base and add the exponents. .
5 + 4 = 9
35 ∙ 34
= 39

19. Simplify each expression.
1) 47 ∙ 45 = 2) 82 ∙ 80 = 3) c3 ∙ c = 4) (5xy2)(-4x3y5) = 5) (3x2)(2x3) =

20. Simplify each expression.
1) 47 ∙ 45 = ) 82 ∙ 80 = 82 3) c3 ∙ c = c4 4) (5xy2)(-4x3y5) = -20x4y7 5) (3x2)(2x3) = 6x5

21. Dividing Exponents

22. What does this expression really mean?
56 ÷ 53

23. What does this expression really mean?
56 ÷ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

24. What does this expression really mean?
56 ÷ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

25. What does this expression really mean?
56 ÷ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

26. What does this expression really mean?
56 ÷ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

27. What does this expression really mean?
56 ÷ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5
= 53

28. What does this expression really mean?
56 ÷ 53
= 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5
= 53

29. Let’s look at another example.
47 ÷ 42

30. Let’s look at another example.
47 ÷ 42
4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ ∙ 4

31. Let’s look at another example.
47 ÷ 42
4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ ∙ 4

32. Let’s look at another example.
47 ÷ 42
4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ ∙ 4

33. Let’s look at another example.
47 ÷ 42
4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ ∙ 4
= 45

34. Let’s look at another example.
47 ÷ 42
= 45
4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ ∙ 4
= 45

35. From these 3 examples, we can draw a conclusion.
6 – 3 = 3
56 ÷ 53
= 53
When dividing with two bases that are the same, you can simply subtract the exponents.
7 – 2 = 5
47 ÷ 42
= 45

36. Simplify each expression.
47 ÷ 45 =
82 ÷ 80 =
c3 ÷ c =
24k9
6k5 =
5) 32 · 24 · 45 =
31 · 22 · 43

37. Simplify each expression.
47 ÷ 45 = 42
82 ÷ 80 = 82
c3 ÷ c = c2
24k9
6k5 = 4k4 5) 32 · 24 · 45
31 · 22 · 43
= 192