1. Tie to LO Activating Prior Knowledge – Paper
Rewrite each number in exponential notation using 3 as the base.
1. 9
2. 27
3. 81
5. Could -3 be used as a base to rewrite 27? 81? Why or why not?
Tie to LO

2. Today, we will apply the multiplication property of exponents.
Learning Objective
Today, we will apply the multiplication property of exponents.
CFU

3. ex 1 5 4 CFU Concept Development 5 3 =
Multiplying Numbers in Exponential Notation
What does mean?
What does mean? ex
5 3
How did I get 7 as an exponent?
CFU
5·5·5 =
5·5·5∙5·5·5∙5
= 5 7 =
= 5 7
5·5·5·5
CFU

4. Concept Development – Notes #1
CFU

5. Concept Development – Notes #2 Non-example (don’t do)
Multiplying Powers
Rules:
Must have the same base.
Keep the base.
Add the exponents.
Example:
𝟑 𝟐 · 𝟑 𝟓 = 𝟑 𝟐+𝟓 = 𝟑 𝟕
Non-example (don’t do)
𝟑 𝟐 · 𝟑 𝟓 ≠ 𝟗 (𝟐+𝟓)
Remember – the base stays the same
CFU

6. Concept Development – In module
In general, if x is any number and m, n, are positive integers, then
𝑥 𝑚 · 𝑥 𝑛 = 𝑥 𝑚+𝑛
because
𝑥 𝑚 × 𝑥 𝑛 = 𝑥⋯𝑥 × 𝑥⋯𝑥 = 𝑥⋯𝑥 =𝑥 𝑚+𝑛
𝑚 𝑡𝑖𝑚𝑒𝑠 𝑛 𝑡𝑖𝑚𝑒𝑠 𝑚+𝑛 𝑡𝑖𝑚𝑒𝑠
CFU

7. Skill Development/Guided Practice – Notes #6
Simplify each expression. Write your answer in exponential form.
6. a • a5 • a4 a
Add exponents. a 10
CFU

8. Skill Development/Guided Practice – Notes #7
Simplify each expression. Write your answer in exponential form.
• 55 • 43 • 52
• 5
4 + 3
5 + 2
Add exponents.
47 • 57
CFU

9. Skill Development/Guided Practice – Notes #8
Simplify each expression. Write your answer in exponential form.
8. 35• 9
35 • 9
35 • 32 3
5 + 2
𝟑 𝟕
CFU

10. Skill Development/Guided Practice – Notes #9
Simplify each expression. Write your answer in exponential form.
9. 23 • 42
23 • 42
42 = 16
23 • 24
23+4 27
CFU

11. Independent Practice – Back of Notes
Exercises 1 – 8 Page s.5
About 5 minutes and then we will review.
CFU

12. Review Independent Practice
– Back of Handout
𝟏𝟒 𝟐𝟑 × 𝟏𝟒 𝟖 =
14 31
(−𝟕𝟐) 𝟏𝟎 ×(−𝟕 𝟐) 𝟏𝟑 =
−72 23
CFU

13. Review Independent Practice
– Back of Handout
𝟓 𝟗𝟒 × 𝟓 𝟕𝟖 =
5 172
(−𝟑) 𝟗 ×(− 𝟑) 𝟓 =
−3 14
CFU

14. Review Independent Practice
– Back of Handout
Let a be a number.
𝒂 𝟐𝟑 · 𝒂 𝟖 =
Let f be a number.
𝒇 𝟏𝟎 · 𝒇 𝟏𝟑 =
𝑎 31
𝑓 23
Let b be a number.
𝒃 𝟗𝟒 · 𝒃 𝟕𝟖 =
𝑏 172
CFU

15. Review Independent Practice
– Back of Handout
8. Let x be a positive integer.
If (− 𝟑) 𝟗 ×(− 𝟑) 𝒙 = (−𝟑) 𝟏𝟒 , what is x?
−3 9+𝑥 = −3 14
Then: 9+𝑥=14
Therefore: 𝑥=5
CFU

16. Independent/Partner Work – Handout
Exercises 9 – 16
About 8 minutes and then we will review.
CFU

17. Review Independent/Partner Practice
– Back of Notes
What would happen if there were more terms with the same base? Write an equivalent expression for each problem?
𝟗 𝟒 × 𝟗 𝟔 × 𝟗 𝟏𝟑 =
9 23
𝟐 𝟑 × 𝟐 𝟓 × 𝟐 𝟕 × 𝟐 𝟗 =
2 24
CFU

18. Review Independent/Partner Practice
– Back of Notes
Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not.
𝟔 𝟓 × 𝟒 𝟗 × 𝟒 𝟑 × 𝟔 𝟏𝟒 =
12. (−𝟒) 𝟐 · 𝟏𝟕 𝟓 · (−𝟒) 𝟑 · 𝟏𝟕 𝟕 =
𝟏𝟓 𝟐 · 𝟕 𝟐 · 𝟏𝟓·𝟕 𝟒 =
* 𝟐 𝟒 × 𝟖 𝟐 =
6 19 ∙ 4 12
−4 5 ∙ 17 12
15 3 ∙ 7 6
2 4 ∙64=
2 4 ∙ 2 6
= 2 10
CFU

19. Review Independent/Partner Practice
– Back of Notes
Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not.
𝟑 𝟕 ×𝟗= 𝟓 𝟒 × 𝟐 𝟏𝟏 =
3 7 ∙ 3 2
= 3 9
Not possible because the bases are not the same!
CFU

20. Review Independent/Partner Practice
– Back of Notes
*17. Let x be a number. Simplify the expression of the following number:
(𝟐𝒙 𝟑 ) (𝟏𝟕𝒙 𝟕 )
CFU

21. Review Independent/Partner Practice
– Back of Notes
*18. Let a and b be numbers. Use the distributive law to simplify the expression of the following number:
𝒂 𝒂+𝒃 =
CFU

22. Review Independent/Partner Practice
– Notes
19. Let a and b be numbers. Use the distributive law to simplify the expression of the following number:
𝒃 𝒂+𝒃 =
CFU

23. Review Independent/Partner Practice
– Notes
20.*** Let a and b be numbers. Use the distributive law to simplify the expression of the following number:
(𝒂+𝒃) 𝒂+𝒃 𝒂+𝒃 =
CFU

24. Closure – Back of Notes 4. 𝟑 𝟖 × 𝟑 𝟕 5. 𝟓 𝟑 ×𝟐𝟓 CFU
1. What did we learn today?
2. Why is this important to you?
3. How do you find the new exponent when multiplying numbers in exponential notation with the same base?
4. 𝟑 𝟖 × 𝟑 𝟕
5. 𝟓 𝟑 ×𝟐𝟓
6. Let a and b be positive integers.
𝟐𝟑 𝒂 × 𝟐𝟑 𝒃
CFU