Tie to LO Activating Prior Knowledge – Notes Simplify each expression – write out to find the quotient. 1. 𝟐 𝟑 𝟐 𝟐 = 𝟐·𝟐∙𝟐 𝟐∙𝟐 2. 𝟓 𝟒 𝟓 = 𝟓·𝟓∙𝟓⋅𝟓 𝟓 =2 = 𝟓 𝟑 3. 𝒚 𝟒 𝒚 𝟒 4. 𝒙 𝟓 𝒙 𝟎 = 𝒚·𝒚∙𝒚·𝒚 𝒚·𝒚∙𝒚·𝒚 = 𝒚 𝟎 = 𝒙·𝒙·𝒙⋅𝒙⋅𝒙 𝟏 = 𝒙 𝟓 =𝟏 Tie to LO

Learning Objective Today, we will simplify expressions with negative exponents and apply exponent properties. CFU

Concept Development – Notes #3 Ex 2 - Simplify. x–3 x–3 = 1 𝑥 3 𝒙 𝟐 𝒙 𝟓 = 𝒙·𝒙 𝒙⋅𝒙∙𝒙∙𝒙∙𝒙 = 𝟏 𝒙∙𝒙∙𝒙 = 𝟏 𝒙 𝟑 Or 𝒙 𝟐 𝒙 𝟓 = 𝒙 𝟐−𝟓 = 𝒙 −𝟑 = 𝟏 𝒙 𝟑 CFU

Skill Development/Guided Practice – Notes #6 & 7 Simplify the powers of 10. 6. 10–9 7. z–4 z–4 = 𝟏 𝒛 𝟒 10–9 = 1 10 9 CFU

Skill Development/Guided Practice - Whiteboard Simplify the powers of 10. Write the power under 1; change the sign of the exponent. b. r–2 a. 10–3 r–2 = 𝟏 𝒓 𝟐 = 1 10 3 10–3 CFU

Skill Development/Guided Practice – Notes #8 & 9 Simplify each expression. Write your answer in exponential form. 8. 𝟖 𝟓 𝟖 𝟏𝟎 9. (− 𝟓) 𝟑 (−𝟓) 𝟑 𝟖 𝟓−𝟏𝟎 (−𝟓) 𝟑−𝟑 (−𝟓) 𝟎 𝟖 −𝟓 𝟏 𝟖 𝟓 𝟏 CFU

𝟏 𝒂 CFU 𝒂 𝟔−𝟕 (−𝒙) 𝟎−𝟓 (−𝒙) −𝟓 𝒂 −𝟏 𝟏 (−𝒙) 𝟓 c. 𝒂 𝟔 𝒂 𝟕 Skill Development/Guided Practice – Whiteboard Simplify each expression. Write your answer in exponential form. c. 𝒂 𝟔 𝒂 𝟕 d. (− 𝒙) 𝟎 (−𝒙) 𝟓 𝒂 𝟔−𝟕 (−𝒙) 𝟎−𝟓 (−𝒙) −𝟓 𝒂 −𝟏 𝟏 (−𝒙) 𝟓 𝟏 𝒂 CFU

Skill Development/Guided Practice – Notes #10 & 11 Simplify each expression. Write your answer in exponential form. 10. 𝟕 𝟑 ·𝟕 −𝟖 ⋅ 𝟕 𝟑 11. (𝒃 𝟓 ) −𝟐 𝒃 𝟓(−𝟐) 𝟕 𝟑+ −𝟖 +𝟑 𝒃 −𝟏𝟎 𝟕 −𝟐 𝟏 𝒃 𝟏𝟎 𝟏 𝟕 𝟐 CFU

𝟏 𝒙 𝟐 𝟑 𝟎(−𝟐) CFU e. 𝒙 −𝟓 ⋅ 𝒙 𝟒 ∙𝒙 −𝟏 𝒙 −𝟓+𝟒+ −𝟏 𝟑 𝟎 𝒙 −𝟐 𝟏 Skill Development/Guided Practice – Whiteboard Simplify each expression. Write your answer in exponential form. e. 𝒙 −𝟓 ⋅ 𝒙 𝟒 ∙𝒙 −𝟏 f. ( 𝟑 𝟎 ) −𝟐 𝟑 𝟎(−𝟐) 𝒙 −𝟓+𝟒+ −𝟏 𝟑 𝟎 𝒙 −𝟐 𝟏 𝟏 𝒙 𝟐 CFU

Skill Development/Guided Practice – Notes #12 & 13 Simplify each expression. Write your answer in exponential form. 13. 𝒙 −𝟐 ∙ 𝒚 𝟑 𝒙 −𝟑 ∙𝒚 𝟑 12. 𝒃 −𝟕 × 𝒃 𝟎 = 𝒙 −𝟐−(−𝟑) 𝒚 𝟑−𝟑 = 𝑏 −7 = 1 𝑏 7 = 𝒙 𝟏 𝒚 𝟎 = 𝒙 CFU

Skill Development/Guided Practice – Whiteboard Simplify each expression. Write your answer in exponential form. h. 𝟑 −𝟒 ∙ 𝒛 𝟕 𝟑 𝟎 ∙𝒛 𝟓 g. 𝒅 −𝟏 · 𝒅 𝟎 ∙𝒅 −𝟐 = 𝟑 −𝟒−𝟎 𝒛 𝟕−𝟓 = 𝟑 −𝟒 𝒛 𝟐 = 𝑑 −1+0+(−2) = 𝒛 𝟐 𝟑 𝟒 = 𝑑 −3 = 1 𝑑 3 CFU

Skill Development/Guided Practice – Notes #14 & 15 Simplify each expression. Write your answer in exponential form. 15. (𝟐 𝒚 𝟐 𝒛 𝟎 ) −𝟐 14. (𝟐 𝒃 −𝟕 ) −𝟏 = 𝟐 𝟏(−𝟐) 𝒚 𝟐(−𝟐) 𝒛 𝟎(−𝟐) = 2 1(−1) 𝑏 (−7)(−1) = 𝟐 −𝟐 𝒚 −𝟒 𝒛 𝟎 = 2 −1 𝑏 7 = 𝟏 𝟐 𝟐 𝒚 𝟒 = 𝑏 7 2 CFU

=3 (1)−2 ⋅ 𝑣 (3)−2 =3 −2 ⋅ 𝑣 −6 = 1 3 2 𝑣 6 = 7 6 =𝒉 𝟎(−𝟑) × 𝟕 −𝟐 (−𝟑) Skill Development/Guided Practice – Whiteboard Simplify each expression. Write your answer in exponential form. i. ( 𝒉 𝟎 × 𝟕 −𝟐 ) −𝟑 j. (𝟑 𝒗 𝟑 ) −𝟐 =𝒉 𝟎(−𝟑) × 𝟕 −𝟐 (−𝟑) =3 (1)−2 ⋅ 𝑣 (3)−2 =3 −2 ⋅ 𝑣 −6 =𝒉 𝟎 𝟕 𝟔 = 1 3 2 𝑣 6 = 7 6 CFU

Independent Practice – Module page S.18 About 4 minutes and then we will review. Write an equivalent expression, in exponential notation, to the one given and simplify as much as possible. 1 5 3 1 𝑥 3 5. 5 −3 8. 𝑥 −3 6. 1 8 9 9. 1 𝑥 9 8 −9 𝑥 −9 𝑥 𝑦 4 3 2 4 10. 𝑥 𝑦 −4 7. 3∙ 2 −4 CFU

Independent Practice – Module pg. S.19 Write an equivalent expression, in exponential notation, to the one given and simplify as much as possible. 𝟏𝟗 𝟐 𝟏𝟗 𝟓 = 11. 12. 17 16 17 −3 = 19 2−5 17 16−(−3) 19 −3 17 19 1 19 3 CFU

Closure - Notes CFU 1. What did we learn today? 2. Why is this important to you? 3. How do I simplify a negative exponent? 4. Simplify 𝒇 −𝟒 5. Simplify 𝒂𝒃 −𝟏 6. Solve for z (𝒚 𝒛 ) −𝟐 = 𝒚 𝟏𝟒 CFU