Algebra 1 Honors Lesson

Radical Roots: Connecting Rational Exponents and Radicals

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9th/10th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.HSN.RN.A.1, CCSS.MATH.CONTENT.HSN.RN.A.290 min

Learning Objective

Students will convert between radical and rational exponent notation, apply properties of exponents to simplify expressions with fractional exponents, and simplify radical expressions by extracting perfect-power factors.

Lesson Overview

Students discover the relationship between rational exponents and radical notation, then build fluency converting between forms and simplifying expressions. Tasks progress from reading radical notation to simplifying complex expressions with fractional exponents.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Erasers or paper towels
Printed consolidation note sheet (one per student)
Pencils

Scaffolded Task Progression

1Task 1

Evaluate each expression. No calculator.
a)

25

327

416

532

2Task 2

Rewrite each radical using a rational exponent. The first one is started for you.

x = x^{1/2}

← index 2, so denominator is 2
a)

3 x = x^{?}

4 x = x^{?}

5 x = x^{?}

n x = x^{?}

3Task 3

Now the numerator is not 1. Rewrite each using a rational exponent. Example:

3 x^{2} = x^{2/3}

← power is numerator, root is denominator
a)

3 x^{4}

5 x^{2}

x^{3}

4 x^{7}

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