# Ch 1: Common Core HS Math: Rational Exponents

These video lessons guide you step-by-step through learning about what rational exponents are to using rational exponents in equations and arithmetic problems. This common core math chapter can be used to enhance your classroom experience in the subject.

Standard: 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 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)3 = 5( to the 1/3)3 to hold, so (5 to the 1/3)3 must equal 5. (CCSS.Math.Content.HSN-RN.A.1)

Standard: Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CCSS.Math.Content.HSN-RN.A.2)

Standard: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. (CCSS.Math.Content.HSN-RN.B.3)

A clear understanding of rational exponents enables students to identify rational and radical numbers as well as solve arithmetic problems using rational and irrational numbers. Students who comprehend the elements of rational exponents will be able to simplify expressions and find the distributive properties of expressions using rational exponents.

The lessons in this standard cover the following topics:

• The five main exponent properties
• Zero and the negative exponent
• Simplifying expressions with exponents
• Different types of numbers
• Rationalizing the denominator
• Addition, subtraction and multiplication with rational exponents
• Dividing expressions with rational exponents
• The distributive property and expressions with rational exponents
• Sums and products of rational and irrational numbers

Students show they've mastered this standard by being able to correctly identify the properties of rational exponents and perform mathematical equations based on the types of numbers used in the expressions. This standard and these lessons can prepare them for college and careers, such as in financial, construction and engineering industries.

### How to Use These Lessons in Your Classroom

The following are some tips on how you can incorporate these lessons on rational exponents into your curriculum to help meet the common core standards:

#### Exponent Identification Lessons

Have students watch the video lessons that cover the different types of numbers, radical and rational exponents and the main properties of exponents in the classroom or as homework assignments. Create two or three rewritten rational exponents, and pass one out to each student. Have the students group themselves based on whether their assigned rational exponents are the same.

#### Simplifying Expressions Lessons

Watch the Simplifying Expressions with Rational Exponents lesson in the classroom or assign it for homework. Go over the practice lesson on the same topic together in class.

#### Pre-Quiz and Post-Quiz Lessons

Have students take the quizzes for the Multiply and Divide Expressions with Rational Exponents and Add and Subtract Expressions with Rational Exponents to introduce the concepts of arithmetic problems using rational expressions. Watch the video lessons, then have students re-take the quizzes to assess their comprehension.

19 Lessons in Chapter 1: Common Core HS Math: Rational Exponents
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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More Exams
There are even more practice exams available in Common Core HS Math: Rational Exponents.

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### Other Chapters

Other chapters within the Common Core Math - Number & Quantity: High School Standards course

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