Section B Section B Checkpoint

Problem 1

Select all the expressions that are equivalent to 252^{5}.
A
2⋅2⋅2⋅2⋅22\boldcdot2\boldcdot2\boldcdot2\boldcdot2
B
5⋅55\boldcdot5
C
101052\frac{10^{10}}{5^2}
D
101055\frac{10^{10}}{5^5}
E
2-2⋅272^{\text-2}\boldcdot2^7
F
23⋅2523\frac{2^3\boldcdot2^5}{2^3}
G
-2-5\text-2^{\text-5}
H
20⋅252^0\boldcdot2^5
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Solution
A, E, F, H
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Sample Response
A, E, F, H

Problem 2

Write 45⋅754^5\boldcdot7^5 using a single exponent.

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Solution
28528^5
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Sample Response
28528^5

Problem 3

Explain why 34⋅833^4\boldcdot8^3 cannot be written using a single exponent.
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Solution
Sample response: The expression has 4 factors that are 3 and 3 factors that are 8. Three 3s and three 8s can be regrouped into 3 factors of 3⋅83\boldcdot8, but there will still be 1 extra factor of 3 that cannot be regrouped and, so, this expression cannot be rewritten using a single exponent.
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Sample Response
Sample response: The expression has 4 factors that are 3 and 3 factors that are 8. Three 3s and three 8s can be regrouped into 3 factors of 3⋅83\boldcdot8, but there will still be 1 extra factor of 3 that cannot be regrouped and, so, this expression cannot be rewritten using a single exponent.