# Rewrite and simplify using rational exponents

I assign different expert groups different sections of the worksheet. After students have completed the Warm Up, I review it with them. The benefit to this assignment lies in its flexibility. The lesson goes much smoother if students are comfortable with working with exponents and this entry ticket has the intent of getting students to that point.

In the last section I present to students how to write as a single rational exponent by finding a common denominator for the exponents and then simplifying.

For problems students are struggling on, they can utilize the experts on those particular types of problems for support and guidance.

After answering any questions I give students rewrite and rewrite and simplify using rational exponents using rational exponents minute to revise and add additional details to their notes. As an alternative, students could use an online math dictionary. I explicitly teach students the difference between Brick and Mortar Words as I firmly believe students need to be taught what types of conversation and language are valued in school AND how to engage in those skills.

One such source can be found here: Exponential Functions for the unit for homework. For this particular activity I use a teacher-generated worksheet on rewriting radical and rational expressions.

Sometimes partners within the class help each other. I have included two versions of the vocabulary for teachers - one with definitions and one without.

This is also a great opportunity to ask students to reflect on what they have done well and what they need to work on to be successful for the remainder of the class. In most of the Guided Notes I emphasize the vocabulary of rational exponents for students to be able to rewrite expressions between radical and rational exponent form.

First, I like to have students hear alternate methods for solving solutions and to hear from people other than myself on how to solve different types of math problems.

The assignment is also flexible in how it can be used in the classroom. I show problem 8 and problem 9 in the video below. Then use that structure to rewrite it, simplify it, or change forms.

Idea Organizer and Writing Prompt 15 minutes To wrap up the assignment, I have students choose one problem from the worksheet on rewriting a radical expression into a rational expression. During the notes I am asking questions to encourage students to not only write, but also engage in other domains of language - namely listening, reading and speaking.

For example, a teacher might assign the Idea Organizer as an exit ticket to wrap up this lesson or students ca come into class the next day, with the Idea Organizer completed for homework. Students can complete the vocabulary work on iPad minis part of a technology grant for Modeling with Mathematics and Universal Design for Learning in the Math Classroom using a math dictionary to look up the definitions for the terms.

I ask them to complete an Exit Ticket: My role as a teacher shifts to that of a facilitator as the students take on the role of teaching each other. After students watch the first video, I have students explain the steps back as a way to gauge their understanding of the process of rewriting radical and rational expressions using rules of exponents.

I recommend Wolfram Alpha as it provides excellent knowledge, is accurate and also provides good visual examples for many terms.

All students have access to the different tasks of this assignment, and get to hear multiple perspectives and strategies to solve the different types of problems. Expert Groups In this segment, students are all assigned to an Expert Group. Most of the students have not been introduced to rational exponents, and I want them to build a strong vocabulary and understanding of how the exponential expression and rational exponents are structured.

The Power Property - multiply exponents times exponents of powers to other powers.

They can then work on writing up their response in a well-polished multi-paragraph response. Writing also can help students better understand the content because the process requires students to translate their ideas and understanding into another form Exit Ticket:Students review basic rules of exponents and use these rules to rewrite radical and rational exponents!

Plan your minute lesson in Math or Exponents with helpful tips from Jason Colombino LESSON 1: Rewriting Radical and Rational Exponents (Plus Exponents Review) LESSON 2: Rewriting Radical and Rational Exponents.

Rewrite the entire expression using rational exponents.

Now you have all the properties of exponents available to help you to simplify the expression: x 1/2 (x 2/3 – x 4/3). Distribute to get rid of the parentheses. Demonstrates how to simplify fractions containing negative exponents. Provides worked examples, showing how the same exercise can be correctly worked in more than one way.

Warns against confusing "minus" signs on numbers and "minus" signs in exponents. Simplify using positive exponents. Always reduce the fractions to lowest terms. We want to rewrite these using positive exponents. Remember, if it's negative in the numerator, it flips to the. Radicals and Rational Exponents.

Learning Objectives. Evaluate and simplify square roots. Rationalize a denominator that contains a square root. Rewrite a radical expression using rational exponents. To simplify a square root, we rewrite it such that there are no perfect squares in the radicand.

There are several properties of square roots. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences.

Rewrite and simplify using rational exponents
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