Free Printable WorksheetMathGrade 8Math Curriculum8.EE.A.1

8.25 Using the Quotient of Powers Property Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.25 Using the Quotient of Powers Property. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.25 Using the Quotient of Powers Property - Which simplified expression correctly applies the quotient of powers property? (CCSS 8.EE.A.1; CA 8.EE.A.1; MA 8.EE.A.1)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.25 Using the Quotient of Powers Property skill assessments:

Problem 1Difficulty: Hard
Which explanation best justifies that x6 / x9 = 1/x3?
AAdd the exponents to get x15.
BSubtract 9 - 6 and keep the answer in the numerator.
CSubtract 6 - 9 to get x^-3, then rewrite x^-3 as 1/x3.
DKeep the larger exponent and write x9.
Solution & Explanation:The quotient of powers property gives x^(6 - 9) = x^-3. A negative exponent means reciprocal, so x^-3 = 1/x3.
Problem 2Difficulty: Hard
Evaluate 211 / (23 / 25).
Solution & Explanation:First simplify the denominator: 23 / 25 = 2^(3 - 5) = 2^-2 = 1/4. Then 211 divided by 1/4 is 2^(11 - (3 - 5)) = 213 = 8192.
Problem 3Difficulty: Hard
Which expression is equivalent to 96c11d3 / 12c6d9?
A8c5d12
B8d6/c5
C8c5/d6
D8c17d12
Solution & Explanation:Divide the coefficients first: 96 / 12 = 8. Then subtract exponents for each variable: 11 - 6 = 5 on c; 3 - 9 = -6 on d. Any negative exponent moves to the denominator, so the simplified result is 8c5/d6.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.EE.A.1 (Primary standard selected for prompt fields: CCSS 8.EE.A.1. Skill statement: Which simplified expression correctly applies the quotient of powers property? Associated standards listed with this skill: CCSS 8.EE.A.1; CA 8.EE.A.1; MA 8.EE.A.1. Use this embedded wording as the best available supporting standard description for this workflow.).

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