G8

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

Input/Model

(Teacher Presents)

Directions: Simplify. Write solution in standard form.

1. 
   

25

22

Solution:

Expanded Form: Using Properties:

• 2 ⋅^2 2∙2⋅^2 ⋅^2 ⋅^2

•

2

2 ⋅

2

2 ⋅

2⋅2⋅2

1 = 2

(^3)

• 
  


• 
  

2

2 ⋅

2

2 ⋅

2⋅2⋅2

1 = 2

(^3)

• 23 = 8
  
  
  • 2
  
  
  
  

5

22 = 2

5−2

• 23 = 8

Teacher Talking Points:

• How many factors are in the numerator?


• How many factors are in the denominator?


• How many common factors are there between the denominator and the numerator?


• Remember a common factor in the numerator and the denominator such as^22 is equivalent to 1.


• How many factors are left once you removed the common factors?

2. 
   

(− 3 )^4 ⋅ (− 3 )^3

(−3)^5

Solution:

Expanded Form: Using Properties:

• (−^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

Important: There must be parentheses around the (–3) to have the meaning of –3 • –3 • –3. If there are no parentheses, –3^3 ,

means –3 • 3 • 3 (only one negative sign). Although the value is the same in this problem, the clarification needs to be made

clear. If the exponent is an even number, the value will not be the same.

Teacher Talking Points:

• How many factors are in the numerator?


• How many factors are in the denominator?


• How many common factors are there between the denominator and the numerator?


• Remember a common factor in the numerator and the denominator such as −3−3 is equivalent to 1.


• How many factors are left once you removed the common factors?