Free Printable WorksheetMathAlgebra IIMath CurriculumN-RN.1–2

ALG2.28 Converting Between Radical and Exponent Forms Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.28 Converting Between Radical and Exponent Forms. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.28 Converting Between Radical and Exponent Forms - Select the correct conversion for between radical form, rational exponent form, and exponential form using exponent properties. Associated source-listed standards: CCSS N-RN.1–2; CA CCSSM N-RN.1–2; MA 2017 N-RN.1–2; NY NGLS N-RN.1–2; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.28 Converting Between Radical and Exponent Forms skill assessments:

Problem 1Difficulty: Mastery
Assume x > 0 and y > 0. Which exponent form is equivalent to the 4th root of x5 y3 multiplied by the square root of y?
Ax^(5/2)y^(3/2)
Bx^(5/4)y^(3/4)
Cx^(5/4)y^(7/4)
Dx^(5/4)y^(5/4)
Solution & Explanation:The 4th root gives x^(5/4)y^(3/4). The square root of y is y^(1/2), and 3/4 + 1/2 = 5/4.
Problem 2Difficulty: Mastery
Assume r > 0. Write ((the 3rd root of r2)5) divided by the 6th root of r as a single exponent.
Ar^(9/6)
Br^(7/6)
Cr^(19/6)
Dr^(21/6)
Solution & Explanation:The numerator is (r^(2/3))5 = r^(10/3). Subtract 1/6 for the denominator: 10/3 - 1/6 = 19/6.
Problem 3Difficulty: Mastery
Assume p > 0 and q > 0. Which radical expression matches p^(5/6)q^(1/3) when written with a common root index?
Athe cube root of p5 q
Bthe 6th root of p5 q2
Cthe 6th root of p5 q
Dthe 6th root of p2 q5
Solution & Explanation:Use denominator 6 as the common index. Rewrite q^(1/3) as q^(2/6), so the combined radical is the 6th root of p5 q2.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard N-RN.1–2 (Select the correct conversion for between radical form, rational exponent form, and exponential form using exponent properties. Associated source-listed standards: CCSS N-RN.1–2; CA CCSSM N-RN.1–2; MA 2017 N-RN.1–2; NY NGLS N-RN.1–2; TX TEKS Algebra II: §111.40.).

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