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Copyright © Swun Math Grade 8 Unit 2 Lesson 3 C TE

Homework

Unit 2 · Lesson 3: Divide Exponents

Objective: I will use the expanded form to show the division of exponents.

Vocabulary Steps:

Properties of Exponents

Power to Power (an)m= anm (Multiply)

Multiply (Like Bases) am⋅an= am+n (Add)

Power of a Product anbn=(ab)n (Keep)

Division (Like Bases)

an

am= a

n−m (Subtract)

1. Identify the base(s) and exponent(s).


2. Write the exponential notation in expanded
   form.


3. Cancel all fractions that are equivalent to 1.
   3
   3 = 1 and^

푎푎

푎푎= 1^

4. Simplify.


5. Check using the properties of exponents.

Example # 1

Directions: Simplify. Write solution in standard form

25

22

Solution:

Expanded Form: Property:

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

2∙2^

• 22 ⋅^22 ⋅2⋅2⋅2 1 = 2^3


• 
  


• 22 ⋅^22 ⋅2⋅2⋅2 1 = 2^3


• 283 =
  
  
  • 2
  
  
  
  

5

22 = 2

5−2

• 23 = 8

Example # 2

(− 3 )^4 ⋅ (− 3 )^3

(− 3 )^5

Solution:

Expanded Form: Property:

• (−^3 )∙((−−3^3 ))∙∙((−−3^3 ))∙∙((−−3^3 ))∙∙((−−3^3 ))∙∙((−−3^3 ))∙(−^3 )^

• (−3)∙((−3−3))∙∙((−3−3))∙∙((−3−3))∙∙((−3−3))∙∙((−3−3))∙(−3)^ →((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙(−3) 1 ∙(−3)

• ((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙(−3) 1 ∙(−3)

• ((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙((−3−3))∙(−3) 1 ∙(−3)=(− 3 )^2


• (− 3 )^2 = 9
  
  
  • (−3)
  
  
  
  

(^4) ∙(−3) 3
(−3)^5 =
(−3)^4 +^3
(−3)^5 =
(−3)^7
(−3)^5

• (−3)

7

(−3)^5 = (−3)

7−5

• (−3)^2 = 9

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