Worksheet

Student Opinion Survey: Exponent Audit

Apply integer exponent rules to numerical expressions and check calculations for a school newspaper’s student opinion survey.

Grade 8MathInteractive · Printable

Aligned to8.EE.A.1

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students use product, quotient, and power properties to write equivalent numerical expressions.
Students evaluate numerical expressions with zero and negative integer exponents.
Students apply exponent properties to survey counts, response codes, and file sizes.

How to use

Use after introducing integer exponent properties. Have students show their rewrites on separate paper, then discuss the final file-size claim.

Curriculum

Common Core standard covered

8.EE.A.1

Know and use the properties of integer exponents to write equivalent numerical expressions.

Preview

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Name Date

Student Opinion Survey: Exponent Audit

Use integer exponent properties to check the school newspaper’s survey calculations.

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.

Complete the equivalent expression by writing the missing exponent.

6⁴ × 6² = 6ⁿ, so n =

Which expression is equivalent to 7² ÷ 7⁵?

A. 7⁻³
B. 7³
C. 1⁻³
D. 7⁷

Which expression is equivalent to (4²)³?

A. 12²
B. 4⁵
C. 4⁶
D. 4⁸

Evaluate the expression in the staff’s checklist.

13⁰ =

Write the value as a fraction with a positive denominator.

6⁻³ =

Audit the Rewrites

Check the staff’s longer expressions. Pay attention to parentheses, negative exponents, and the base of each power.

Which expression is equivalent to (2 × 3)⁻²?

A. −(2² × 3²)
B. 1/(2² × 3²)
C. 1/(2² + 3²)
D. 1/(2 × 3²)

Evaluate the expression. Write your answer as a fraction in simplest form.

(8/3)⁻² =

Evaluate the expression. The parentheses make the negative number the base.

(−3)⁴ ÷ (−3)² =

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 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 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.