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- HSN-RN.A.1Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5<sup>1/3</sup> to be the cube root of 5 because we want (5<sup>1/3</sup>)<sup>3</sup> = 5<sup>(1/3)3</sup> to hold, so (5<sup>1/3</sup>)<sup>3</sup> must equal 5.
- HSN-RN.A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.

HSN-RN.A.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)3} to hold, so (5^{1/3})^{3} must equal 5.

Exponentials and Logarithms: LOUD and CLEAR!

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This engaging lesson allows the students to apply logarithms to the real world! After finishing the study, students will think twice before playing their music too loud!

Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The Laws of Exponents Still Apply! To Fractional Exponents.

Rational Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:Keep students from being irrational about rational exponents with this lesson.

Introduction to Exponential Functions - Rational Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This multi-faceted lesson creatively activates the students' prior knowledge of exponents in a fun and engaging way - it also includes a âfar-outâ example that leaves them with a hunger to learn âexponentiallyâ more!

Real Number Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:It's not enough to be rational, let's get real with exponents.

An "Exponentially" Rewarding Battle!

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson serves as a âBattleshipâ review of real number exponents (both irrational and rational) as well as solving exponential equations. Students engage in battle while trying to sink a partnerâs fleet of answers!

Discovering Solutions to Exponential Equations

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:Students will be challenged to make use of structure (and experiences in previous lessons) to solve their first exponential equations!

Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson (taking place on the day before spring break) is designed to keep the students engaged â rather than mentally hitting the beach early!

Rewriting Radical and Rational Exponents (Plus Exponents Review)

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students review basic rules of exponents and use these rules to rewrite radical and rational exponents!

Real Number Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This building-block lesson includes a touch of technology, collaboration, and critical thinking as the students further familiarize themselves with the rules of exponents â but more importantly, extend these rules to irrational exponents

Rational Exponents

Algebra II

Â» Unit:

Exponents & Logarithms

Big Idea:Mathematics is all about patterns, and exponents reveal some "power"-ful ones!

Khan Academy and Simplifying Radicals

8th Grade Math

Â» Unit:

Gimme the Base: More with Exponents

Big Idea:We can use prime factorization to break down the number inside a radical sign and then use those factors to simplify the expression.

Properties of Exponents

Algebra II

Â» Unit:

Exponential Functions

Big Idea:Fractional exponents can be used in place of radical symbol. This can make working with radicals easier in some cases.

HSN-RN.A.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)3} to hold, so (5^{1/3})^{3} must equal 5.

HSN-RN.A.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.