# Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.

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## Objective

SWBAT rewrite rational exponents as a radical expression and vice versa, and understand the different structures that are equivalent.

#### Big Idea

The Laws of Exponents Still Apply! To Fractional Exponents.

## Warm Up

10 minutes

This Warm Up should take students about five minutes to complete and for me to review with the class.  The purpose of this Warm up is to introduce students to rational exponents.  I start the questioning in the Warm Up about what is a rational number, and therefore a rational exponent.  Students should be familiar with the Laws of Exponents to apply to these problems.

Some of the Laws of Exponents that are reviewed in the Warm Up are as follows:

1. The Product Property-multiply the coefficients, add the exponents of like bases.
2. The Quotient Property - Divide the coefficients , subtract the exponents of like bases.
3. The Power Property - multiply exponents times exponents of powers to other powers.

After students have completed the Warm Up, I review it with them.  I take questions, and rework any problem that the student needs to see.  Sometimes partners within the class help each other.

## Guided Notes

15 minutes

After reviewing the Warm up and the Laws of Exponents, I work with students on Guided Notes to provide them with new information about rational exponents.  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. Then use that structure to rewrite it, simplify it, or change forms.

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. 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.  I show problem 8 and problem 9 in the video below.

## Independent Practice

15 minutes

The Independent Practice is a way for students to continue practicing after the Guided Notes to build confidence and more knowledge of working with rational exponents.

I break the Independent Practice into 5 different parts: (all answers should be completely simplified).

1.  Rewrite without rational exponents

2.  Rewrite with positive rational exponents

3.  Rewrite with rational exponents

4.  Use rational exponents to simplify

5. Use rational exponents to write as a single radical expression

This Independent Practice is 18  questions long and probably will take the students about 25 minutes.  Rational exponents are new to most students and I wanted to give students a variety of problems to show different uses of rational exponents.  If students do not complete the Independent Practice or the Exit Ticket, it is assigned as homework.

## Exit Ticket

10 minutes

I hand the Exit ticket to students when they complete the Independent Practice or when there are about five minutes left in class.  I use this Exit Ticket as a quick formative assessment to check for  understanding of what the numerator and the denominator mean in the rational exponent.

I take this Exit Ticket up at the End of Class.  The students did well on this Exit Ticket, and clearly were able to explain the meaning of the parts of a rational exponent.