Tie to LO Activating Prior Knowledge – Paper Rewrite each number in exponential notation using 3 as the base. 1. 9 2. 27 3. 81 4. 243 5. Could -3 be used as a base to rewrite 27? 81? Why or why not? Tie to LO

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

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

Concept Development – Notes #1 CFU

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

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

Skill Development/Guided Practice – Notes #6 Simplify each expression. Write your answer in exponential form. 6. a • a5 • a4 a 1 + 5 +4 Add exponents. a 10 CFU

Skill Development/Guided Practice – Notes #7 Simplify each expression. Write your answer in exponential form. 7. 44 • 55 • 43 • 52 4 • 5 4 + 3 5 + 2 Add exponents. 47 • 57 CFU

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

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

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

Review Independent Practice – Back of Handout 1. 𝟏𝟒 𝟐𝟑 × 𝟏𝟒 𝟖 = 14 31 2. (−𝟕𝟐) 𝟏𝟎 ×(−𝟕 𝟐) 𝟏𝟑 = −72 23 CFU

Review Independent Practice – Back of Handout 3. 𝟓 𝟗𝟒 × 𝟓 𝟕𝟖 = 5 172 4. (−𝟑) 𝟗 ×(− 𝟑) 𝟓 = −3 14 CFU

Review Independent Practice – Back of Handout Let a be a number. 5. 𝒂 𝟐𝟑 · 𝒂 𝟖 = Let f be a number. 6. 𝒇 𝟏𝟎 · 𝒇 𝟏𝟑 = 𝑎 31 𝑓 23 Let b be a number. 7. 𝒃 𝟗𝟒 · 𝒃 𝟕𝟖 = 𝑏 172 CFU

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

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

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. 𝟗 𝟒 × 𝟗 𝟔 × 𝟗 𝟏𝟑 = 9 23 10. 𝟐 𝟑 × 𝟐 𝟓 × 𝟐 𝟕 × 𝟐 𝟗 = 2 24 CFU

Review Independent/Partner Practice – Back of Notes Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not. 11. 𝟔 𝟓 × 𝟒 𝟗 × 𝟒 𝟑 × 𝟔 𝟏𝟒 = 12. (−𝟒) 𝟐 · 𝟏𝟕 𝟓 · (−𝟒) 𝟑 · 𝟏𝟕 𝟕 =   13. 𝟏𝟓 𝟐 · 𝟕 𝟐 · 𝟏𝟓·𝟕 𝟒 = *14. 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

Review Independent/Partner Practice – Back of Notes Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not. 15. 𝟑 𝟕 ×𝟗= 16. 𝟓 𝟒 × 𝟐 𝟏𝟏 = 3 7 ∙ 3 2 = 3 9 Not possible because the bases are not the same! CFU

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

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

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

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

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