1. 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

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

3. 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

4. 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 =
CFU

5. 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 =
10–3
CFU

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

7. 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

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

9. 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

10. Skill Development/Guided Practice – Notes #12 & 13
Simplify each expression. Write your answer in exponential form.
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

11. 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

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

13. =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
= 𝑣 6
= 7 6
CFU

14. 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 −3
8. 𝑥 −3
𝑥 9
8 −9
𝑥 −9
𝑥 𝑦 4
3 2 4
10. 𝑥 𝑦 −4
7. 3∙ 2 −4
CFU

15. 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.
−3 =
19 2−5
17 16−(−3)
19 −3
17 19
CFU

16. 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