Activating Prior Knowledge – Handout Solve for x. 1. 4 5 · 4 3 = 4 𝑥 2. 3 2 ×3= 3 𝑥 4. 8 𝑥 · 8 3 = 8 8 3. 5 6 × 5 𝑥 = 5 12 Tie to LO

Today, we will apply properties of exponents. Learning Objective Today, we will apply properties of exponents. CFU

Concept Development (follow notes) Dividing Powers What does 10 5 mean? What does 10 3 mean? CFU ex 1 10 5 1 1 1 = 10 · 10 ·10 ·10 ·10 = 10 2 = 10 5−3 = 10 2 10 3 1 1 1 10 · 10 · 10 How did I get 2 as an exponent? What does 𝑥 2 mean? What does 𝑥 mean? ex 2 𝑥 2 1 = x · x = 𝑥 1 = 𝑥 2−1 = 𝑥 1 x 𝑥 1 How did I get 1 as an exponent? CFU

Concept Development – Notes #1 CFU

Concept Development – Notes #2 Non-example (don’t do) Dividing Powers Rules: Must have the same base. Keep the base. Subtract the exponents. Example: 𝟒 𝟓 𝟒 𝟑 = 𝟒 𝟐 = 𝟒 𝟓−𝟑 Non-example (don’t do) 𝟑 𝟑 𝟐 𝟑 ≠ 𝟏 𝟑 Remember – you need the same base for this property. CFU

Concept Development – Notes #3 3. In general, if x is nonzero and m, n, are positive integers, then 𝑥 𝑚 𝑥 𝑛 = 𝑥 𝑚−𝑛 , 𝑖𝑓 𝑚>𝑛 𝑠𝑖𝑛𝑐𝑒 𝑚>𝑛, then there is a positive integer l, so that m = n + l. 𝑥 𝑚 𝑥 𝑛 = 𝑥 𝑛+𝑙 𝑥 𝑛 = 𝑥 𝑛 ∙ 𝑥 𝑙 𝑥 𝑛 by 𝑥 𝑚 𝑥 𝑛 = 𝑥 𝑚+𝑛 = 𝑥 𝑙 by equivalent fractions = 𝑥 𝑚−𝑛 because m = n + l implies l = m – n Therefore, 𝑥 𝑚 𝑥 𝑛 =𝑥 𝑚−𝑛 , 𝑖𝑓 𝑚>𝑛 CFU

Skill Development/Guided Practice – Notes #4 & 5 Simplify each expression. Write your answer in exponential form. 4. 𝟏𝟎 𝟖 𝟏𝟎 𝟓 5. 𝟑 𝟕 𝟑 𝟑 Subtract exponents. 8 - 5 𝟏𝟎 7 - 3 𝟑 Subtract exponents. 3 4 𝟏𝟎 𝟑 CFU

Skill Development/Guided Practice – Notes #6 & 7 Simplify each expression. Write your answer in exponential form. 6. 2 3 4 2 3 2 7. (− 𝟓) 𝟖 (−𝟓) 𝟒 CFU

Skill Development/Guided Practice – Notes #8 & 9 Simplify each expression. Write your answer in exponential form. 8. 𝟐 𝟖 𝟒 9. 𝒙 𝟏𝟓 𝒙 𝟖 CFU

Independent Practice – Back of Notes About 5 minutes and then we will review. CFU

Review Independent Practice – Back of Notes 10. 7 9 7 6 11. (−5) 16 (−5) 7 CFU

Review Independent Practice – Back of Notes 12. 8 5 9 8 5 2 13. 13 5 13 4 CFU

Review Independent/Partner Practice – Back of Notes Let a, b be nonzero numbers. What is the following number? 7. 𝑎 𝑏 9 𝑎 𝑏 2 CFU

Review Independent/Partner Practice – Back of Notes Let x be a nonzero number. What is the following? 8. 𝑥 5 𝑥 4 CFU

Review Independent/Partner Practice – Back of Notes Can the following be simplified? If yes, write an equivalent expression for each problem. If not, explain why not. 9. 2 7 4 2 10. 𝟑 𝟐𝟑 𝟐𝟕 CFU

Review Independent/Partner Practice – Back of Notes Can the following be simplified? If yes, write an equivalent expression for each problem. If not, explain why not. 11. 3 5 ∙ 2 8 3 2 ∙2 3 12. (−2) 7 ∙ 95 5 (−2) 5 ∙95 4 CFU

Review Independent/Partner Practice – Back of Notes *13. Let x be a number. Simplify the expression of each of the following numbers: a. 5 𝑥 3 3𝑥 8 b. 5 𝑥 3 − 4𝑥 6 c. 5 𝑥 3 11𝑥 4 CFU

Closure – Back of Notes 4. 𝟓 𝟖 𝟓 𝟔 CFU 1. What did we learn today? 2. Why is this important to you? 3. How do you find the new exponent when dividing powers with the same base? 4. 𝟓 𝟖 𝟓 𝟔 5. Let x and y be positive integers and x > y. 𝟏𝟏 𝒙 𝟏𝟏 𝒚 6. 𝟐 𝟏𝟑 𝟖 CFU