2. WB pg. 176

3. WB pg. 176

4. WB pg. 176
Write in exponential form

5. WB pg. 177

6. WB pg. 177

7. WB pg. 177
Evaluating expressions

8. WB pg. 178

9. WB pg. 178
Guided practice

10. WB pg. 178
Guided practice KEY

11. WB pg. 179 Independent practice

12. WB pg. 179 Independent practice KEY

13. WB pg. 179 Independent practice

14. WB pg. 179 Independent practice KEY

15. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power.
Exponent
Base 7 2

16. The factors of a power, such as 74, can be grouped in different ways
The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product.
7 • 7 • 7 • 7 = 74
(7 • 7 • 7) • 7 = 73 • 71 = 74
(7 • 7) • (7 • 7) = 72 • 72 = 74

17. Also know as the laws of exponents:
Product rule (multiply monomials)
Quotient rule (divide monomials)
WB pgs

18. WB pg. 184

19. Product Rule:
Same base, add exponents.

20. WB pg. 184

21. WB pg. 184

22. WB pg. 185

23. WB pg. 185

24. WB pg. 185 KEY

25. WB pg. 186

26. WB pg. 186

27. WB pg. 186 KEY

28. WB pg. 187 Independent practice

29. WB pg. 187 KEY

30. WB pg. 187

31. WB pg. 186 KEY

32. Ex’s : Multiplying Powers with the Same Base
Multiply. Write the product as one power.
1. 66 • 63 6
6 + 3
Add exponents. 6 9
2. n5 • n7 n
5 + 7
Add exponents. n 12

33. Ex’s: Multiplying Powers with the Same Base Continued
Multiply. Write the product as one power.
3. 25 • 2 2
5 + 1
Think: 2 = 2 1 2 6
Add exponents.
• 244 24
4 + 4
Add exponents. 24 8

34. 5. 42 • 44 4 Add exponents. 4 6. x2 • x3 x Add exponents. x You try!!!
Multiply. Write the product as one power.
5. 42 • 44 4
2 + 4
Add exponents. 4 6
6. x2 • x3 x
2 + 3
Add exponents. x 5

35. Cannot combine; the bases are not the same.
You try!!!
Multiply. Write the product as one power.
7. x5 • y2
Cannot combine; the bases are not the same.
x5 • y2
• 417 41
2 + 7
Add exponents. 41 9

36. Same base, subtract exponents.
Quotient Rule:
Same base, subtract exponents.
Notice what occurs when you divide powers with the same base. 5 53 =
5  5  5
5  5  5  5  5
= 5 • 5
= 52

37. Ex’s : Dividing Powers with the Same Base
Divide. Write the quotient as one power. 7 5 3 1. 7
5 – 3
Subtract exponents. 7 2 x 10 9 2. x
10 – 9
Subtract exponents. x
Think: x = x 1

38. 3. 4. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e Ex’s
Divide. Write the product as one power. 9 9 3. 9 2 9
9 – 2
Subtract exponents. 97 e 10 4. e 5 e
10 – 5
Subtract exponents. e 5

39. 5. 4. 3 3 3 Subtract exponents. 32 x x x Subtract exponents. x
You try:
Divide. Write the product as one power. 3 8 5. 3 6 3
8 – 6
Subtract exponents. 32 x 15 4. x 3 x
15 – 3
Subtract exponents. x 12

40. = 1 Zero Exponent Rule Any Base Any base raised to the zero
power (except 0) is ALWAYS
equal to one.
Any Base
= 1

41. Any number divided by itself is always 1.
Why?
Following the Quotient Rule:
Any number divided by itself is always 1.

42. As known as the “power to power rule”
WB pgs

43. WB pg. 192

44. WB pg. 192

45. WB pg. 192

46. WB pg. 193

47. WB pg. 195 Independent practice

48. WB pg. 195 Independent practice KEY

49. Power raised to a power, multiply exponents.
Power to a power Rule :
Power raised to a power, multiply exponents.
Reading Math
(9 ) is read as “nine to the fourth, to the fifth.” 5 4

50. Ex’s: Raising a Power to a Power
Simplify.
1. (54)2
(54)2
= 54 • 2
Multiply exponents.
= 58
2. (67)9
(67)9
= 67 • 9
Multiply exponents.
= 663

51. Ex’s: Raising a power to power
Simplify.
3. (33)4
(33)4
= 33 • 4
Multiply exponents.
= 312
4. (48)2
(48)2
= 48 • 2
Multiply exponents.
= 416

52. Ex’s: Raising a Power to a Power
Simplify.
2 3 12 3 5.
6. (172) 20
(172) 20
Multiply exponents.
Multiply exponents.
2 3
12 • 3 =
= 172 • 20
2 3 36 =
= 1740

53. = = 7. 8. (134) 10 Multiply exponents. Multiply exponents. YOU TRY!!!
Simplify.
1 4 11 2 7.
8. (134) 10
(134) 10
Multiply exponents.
Multiply exponents.
1 4
11• 2 =
= 134 • 10
1 4 22 =
= 1340

54. Power of Product Rule:
Product raised to a power, distribute power to each base.
Evaluate the number(s)/coefficients.
Multiply the exponents.
(2x2y5)3 =
23x2*3y5*3
8x6y15

55. Ex’s : Power to a power rule
16a6b8
1. (4a3b4)2 =
2. (9x5y4)3 =
729x15y12

56. Ex’s: RAISING A POWER TO A POWER
3. (5a5b10)3 =
125a15b30
4. (4x7y9)4 =
256x28y36

57. You TRY!!!
5. (2x4y5)3 =
8x12x15
6. (6a4b6)3 =
216a12b18