Use integer exponent properties to check the school newspaper’s survey calculations.
Answer Key
Check the Calculation Notes
The newspaper staff is preparing a student opinion survey. Check the expressions in its planning notes. Use exponent properties rather than expanding every power.
1.
Complete the equivalent expression by writing the missing exponent.
6⁴ × 6² = 6ⁿ, so n = 6
2.
Which expression is equivalent to 7² ÷ 7⁵?
●A.7⁻³
○B.7³
○C.1⁻³
○D.7⁷
3.
Which expression is equivalent to (4²)³?
○A.12²
○B.4⁵
●C.4⁶
○D.4⁸
4.
Evaluate the expression in the staff’s checklist.
13⁰ = 1
5.
Write the value as a fraction with a positive denominator.
6⁻³ = 1/216
Audit the Rewrites
Check the staff’s longer expressions. Pay attention to parentheses, negative exponents, and the base of each power.
6.
Which expression is equivalent to (2 × 3)⁻²?
○A.−(2² × 3²)
●B.1/(2² × 3²)
○C.1/(2² + 3²)
○D.1/(2 × 3²)
7.
Evaluate the expression. Write your answer as a fraction in simplest form.
(8/3)⁻² = 9/64
8.
Evaluate the expression. The parentheses make the negative number the base.
(−3)⁴ ÷ (−3)² = 9
9.
Which expression is equivalent to (5⁻² × 5⁶) ÷ 5³?
○A.5⁻⁹
○B.5⁻¹
○C.5⁷
●D.5
10.
The editor needs expressions equal to 1/16 for a calculation note. Select every expression that works.
2⁻⁴4⁻²−(2⁴)(1/2)⁴2⁰ ÷ 2³
Apply the Rules to the Survey
Use the survey details to choose or calculate an answer. Explain your reasoning for the final item.
11.
The newspaper plans to survey the same number of students in each participating class. Each student belongs to only one participating class.
Survey Participation Plan
Participating classes
Students per class
2³
2⁴
Which expression gives the total number of students in the plan?
●A.2⁷
○B.4⁷
○C.2¹²
○D.2³ + 2⁴
12.
A survey data file contains 3⁶ bytes of response data. Each completed response uses exactly 3² bytes. The file contains no other data. How many completed responses are in the file?
The file contains 81 completed responses.
13.
A survey has four questions about school activities. Each question has 2³ answer choices, and a student selects exactly one choice per question. Every combination of choices is allowed. How many different completed answer patterns are possible?
There are 4096 possible answer patterns.
14.
A compressed survey file is 2⁻³ times the size of the original file. Sam says, “The exponent is negative, so the compressed file has a negative size.” Explain why Sam is incorrect, and state what fraction of the original size the compressed file has.
A negative exponent means take the reciprocal; it does not make a positive base negative. Since 2⁻³ = 1/2³ = 1/8, the compressed file has a positive size equal to 1/8 of the original size.