1. Activating Prior Knowledge – Notes
Simplify each expression.
1. 𝟓× 𝟏 𝟓 𝟓 𝟕 × 𝟕 𝟓 𝟑 𝟒 ÷ 𝟑 𝟒
= 𝟓 𝟓 =𝟏
= 𝟑𝟓 𝟑𝟓 =𝟏 𝟏
Rewrite using exponents.
∙8 8∙8
5. 𝑥 2 ∙ 𝑥 3 𝑥∙ 𝑥 4
𝒙 𝟓 𝒙 𝟓
𝟖 𝟐 𝟖 𝟐
Tie to LO

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

3. 𝟑. (𝒙𝒚) 𝒏 = 𝒙 𝒏 𝒚 𝒏 1. 𝒙 𝒎 ⋅ 𝒙 𝒏 = 𝒙 𝒎+𝒏 𝟐. (𝒙 𝒎 ) 𝒏 = 𝒙 𝒎𝒏
Concept Development Review – Pair Share
Summarize Properties of exponents
1. 𝒙 𝒎 ⋅ 𝒙 𝒏 = 𝒙 𝒎+𝒏
𝟐. (𝒙 𝒎 ) 𝒏 = 𝒙 𝒎𝒏
𝟒 𝒙 𝒎 𝒙 𝒏 = 𝒙 𝒎−𝒏
𝟑. (𝒙𝒚) 𝒏 = 𝒙 𝒏 𝒚 𝒏
𝟓. 𝒙 𝒚 𝒏 = 𝒙 𝒏 𝒚 𝒏
CFU

4. Concept Development – Notes #1
CFU

5. Concept Development – Notes #2
Zero Exponents
Rule:
The zero power of any nonzero number is equal to 1.
Example:
𝟔 𝟎 = (−𝟐) 𝟎 = 1
Nonexample (no!)
𝟔 𝟎 ≠ (−𝟐) 𝟎 ≠ -2
CFU

6. Concept Development – Notes #3
3. In general, if x is any number and m, n, are integers, then
𝐍𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞
𝐀𝐥𝐠𝐞𝐛𝐫𝐚𝐢𝐜 𝐞𝐱𝐚𝐦𝐩𝐥𝐞
𝑥 𝑚 · 𝑥 𝑛 = 𝑥 𝑚+𝑛
𝑥 𝑚 · 𝑥 0 = 𝑥 𝑚+0
𝑥 𝑚 · 𝑥 0 = 𝑥 𝑚
𝑥 0 =1
CFU

7. Concept Development – Notes #4
4. In general, if x is nonzero and m, n, are positive integers, then 𝑥 𝑚 𝑥 𝑛 = 𝑥 𝑚−𝑛 , 𝑖𝑓 𝑚>𝑛
𝐍𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞
𝐀𝐥𝐠𝐞𝐛𝐫𝐚𝐢𝐜 𝐞𝐱𝐚𝐦𝐩𝐥𝐞
𝑥 𝑚 𝑥 𝑛 = 𝑥 𝑚−𝑛
𝑥 𝑚 𝑥 0 = 𝑥 𝑚−0
𝑥 𝑚 𝑥 0 = 𝑥 𝑚
𝑥 0 =1
CFU

8. Skill Development/Guided Practice – Notes #5 & 6
Simplify each expression. Write your answer in exponential form.
5. 40
= 1
6. (-3)0
= 1
The zero power of any nonzero number is equal to 1.
CFU

9. Skill Development/Guided Practice – Whiteboard
Simplify. b
a. (–8)0
= 1
(–8)0 = 1
Any nonzero number raised to zero power is equal to 1.
CFU

10. Skill Development/Guided Practice – Notes #7 & 8
Simplify each expression. Write your answer in exponential form.
8. 𝒙 𝟐 ∙ 𝒚 𝟑 𝒙∙𝒚 𝟑
= 𝑥𝑦 0
7. 𝒂 𝟑 × 𝒂 𝟎
= x
= 𝑎 3
CFU

11. Skill Development/Guided Practice Review – Notes #9 & 10
Simplify each expression. Write your answer in exponential form.
9. 35• 9
• 42
23 • 42
35 • 9
42 = 16
35 • 32
23 • 24 3
5 + 2
23+4
𝟑 𝟕 27
CFU

12. Skill Development/Guided Practice Review- Whiteboard
Simplify each expression. Write your answer in exponential form.
f. 24 • 8 • 23
e. 53 • 25
24 • 23 • 23
53 • 52 5
3 + 2 2
𝟓 𝟓
210
CFU

13. Skill Development/Guided Practice – Notes #11 & 12
Simplify each expression. Write your answer in exponential form.
(− 𝟓) 𝒂 (−𝟓) 𝒃
CFU

14. Skill Development/Guided Practice – Whiteboard
Simplify each expression. Write your answer in exponential form.
g − −
h 𝟐.𝟑𝟓 𝟕 𝟐.𝟑𝟓 𝒃
= 𝟐.𝟑𝟓 𝟕−𝒃
− 𝟏 𝟓 𝟎 =𝟏
CFU

15. 𝑎 𝒂 𝟏𝟓 CFU (−𝟕) i. (𝒂 𝟑 ) 𝟓 j. ((−𝟕) 𝒂 ) 𝟖 (−𝟕)
Skill Development/Guided Practice Review – Whiteboard
Simplify each expression. Write your answer in exponential form.
i. (𝒂 𝟑 ) 𝟓
j. ((−𝟕) 𝒂 ) 𝟖
3×5 𝑎
a×8
(−𝟕)
𝒂 𝟏𝟓 8a
(−𝟕)
CFU

16. Skill Development/Guided Practice Review – Notes #16
Simplify each expression in exponential notation.
16. (−3 𝑥 3 𝑦 𝑧 2 ) 3
=(−3 𝑥 3 𝑦 𝑧 2 )×(−3 𝑥 3 𝑦 𝑧 2 )×(−3 𝑥 3 𝑦 𝑧 2 )
=[(-3)×(-3)×(-3) ( 𝑥 3 𝑥 3 𝑥 3 )(yyy)( 𝑧 2 𝑧 2 𝑧 2 )]
= (−3) 3 𝑥 9 𝑦 3 𝑧 6
CFU

17. Closure – Back of Notes CFU 1. What did we learn today?
2. Why is this important to you?
3. Write what is the difference between 𝟐𝒙 𝟑 and (𝟐𝒙) 𝟑 ?
4. Simplify 𝟒 𝟏𝟎 𝟒 𝟏𝟎 ∙ 𝟕 𝟎
5. Let a and b be two numbers. Use the distributive law and the definition of zeroth power to show that the numbers (𝒂 𝟎 + 𝒃 𝟎 )𝒂 𝟎 and (𝒂 𝟎 + 𝒃 𝟎 )𝒃 𝟎 are equal.
CFU