G8

Copyright © Swun Math Grade 8 Unit 2 Lesson 7 P TE

Challenge Problems

Directions: Solve.

1. Simplify the following expression using
   two different methods.
   푑푑^8 • 푑푑–^5
   푑푑^6

What do you notice about the solutions?

Solution:

Various ways to simplify the expression.

1 st Strategy

The bases are the same, so add the exponents in the

numerator and then subtract the exponents with the

denominator.

• 푑푑

8+(– 5 )

푑푑^6 =

푑푑^3

푑푑^6

• 푑푑

3

푑푑^6 = 푥푥

3−6

• 푑푑−3
  2 nd Strategy
  Use expanded form and cancel the common factors.


• 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑

– (^1) • 푑푑– (^1) • 푑푑– (^1) • 푑푑– (^1) • 푑푑– 1
푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑^ change the five
negative exponents so they are positive.
• (^) 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑푑푑 • • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑푑푑 • • 푑푑 • 푑푑^ 푑푑 • 푑푑 (now cancel common factors)
• (^) 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑푑푑 • • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑 • 푑푑푑푑 • 푑푑 = 푑푑^13

• The solutions are the same.
  2. Find and explain the error.
  
  
  • 3푚푚–^4
  
  
  
  


• 3푚푚• – 3푚푚• – 3푚푚• – 3푚푚

1

• 12푚푚

Solution:

The exponent belongs to the variable only. The

expression should have been written the following

way:

−3푚푚 4 표표표표−푚푚^34

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.

* MP4: Apply mathematics in everyday life.

Using the digits 0-9, find at least 3 solutions to the problem below.

푥푥⋅푥푥−

푥푥

= 1