Section C Section C Checkpoint

Problem 1

Decide whether each equation is true or false. Explain how you know.

  1. 24=2⋅42^4=2 \boldcdot 4

  2. 3⋅34=353 \boldcdot 3^4 = 3^5

  3. 2⋅32=622 \boldcdot 3^2 = 6^2

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Solution
  1. False. Sample reasoning:  16=816=8 is not true.
  2. True. Sample reasoning: Each side is 3⋅3⋅3⋅3⋅33 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3.
  3. False. Sample reasoning: 18=3618=36 is not true.
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Sample Response
  1. False. Sample reasoning:  16=816=8 is not true.
  2. True. Sample reasoning: Each side is 3⋅3⋅3⋅3⋅33 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3.
  3. False. Sample reasoning: 18=3618=36 is not true.

Problem 2

Find the value of 7+x37+x^3 when xx is 2.
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Solution

15. Sample reasoning:

7+x37+237+8157 + x^3 \\ 7 + 2^3 \\ 7 + 8 \\15

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Sample Response

15. Sample reasoning:

7+x37+237+8157 + x^3 \\ 7 + 2^3 \\ 7 + 8 \\15