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

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

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

4. Concept Development – Notes #1
CFU

5. 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

6. 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

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

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

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

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

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

12. Review Independent Practice
– Back of Notes
CFU

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

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

15. 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.
𝟑 𝟐𝟑 𝟐𝟕
CFU

16. 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.
∙ ∙ (−2) 7 ∙ (−2) 5 ∙95 4
CFU

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

18. 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?
𝟓 𝟖 𝟓 𝟔
5. Let x and y be positive integers and x > y.
𝟏𝟏 𝒙 𝟏𝟏 𝒚
𝟐 𝟏𝟑 𝟖
CFU