# Laws of Exponents Three: Quotient of a Power & Power of a Quotient

Demonstrate to your students how to solve problems when variables and exponents are involved.

Once the students have learned the basics of exponents, (base, exponent, power, factor) and how to multiply two or more powers that have the same base, now students will learn how to raise exponents to a power when finding the quotient.

**Common Core State Standards**

A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions

**Mathematical Practice(s):** 2. Reason abstractly and quantitatively.

**Learning Target(s)**

- I can explain why equivalent expressions are equivalent.
- I can look for and identify clues in the structure of expressions in order to rewrite it another way.

**Essential Question(s)**

Why structure expressions in different ways?

**Vocabulary:** monomial, equivalent expressions, base, exponent, power, factor, quotient

## Lesson

Notes:

- Review the vocabulary.
**Add to the Foldable**.- Write Quotient of Powers on the tab below Power of a Product and provide a basic example. Ex: b
^{15}/ b^{7}= b^{8} - Now lift up the tab and write on the top portion – Subtract exponents (numerator – denominator) and the answer goes in the numerator. (Same Base). *See negative exponents if necessary. On the bottom portion that says, “Quotient of Powers”, provide an example and explain the example in detail.
- (Continual reminder): if no exponent is written, the exponent is one (1).
- Write Power of a Quotient on the tab below Quotient of Powers and provide a basic example. Ex: (c/d)
^{5}= c^{5}/ d^{5} - Now lift up the tab and write on the top portion – Raise the numerator and the denominator to the power (exponent). On the bottom portion that says, “Power of a Quotient”, provide an example and explain the example in detail.
- REMINDER: Inform students that the denominator should not equal zero.

*** Now you have the basis of your lesson and you can move on to Guided Practice.**

**Guided Practice**: 3-6 practice problems. You can do 1 or 2 problems with the students at the board (Smart Board, Elmo, etc.) and then put them in small groups of no more than 3 to do the rest. These problems can be pulled from any textbook or other resource.

**Independent Practice:** Approximately 5 problems to be done alone.

**Closure/Review:** Ask 1-3 questions relating to today’s lesson to be answered by the class as a whole. This will give you a general idea of the class’ understanding of today’s topic.

**Exit Ticket:** This is to be done the last 3-5 minutes of class and given to you (by hand or in a designated area of your room) as they leave class. Possible question(s): By drawing a picture or some sort of representation, explain how the quotient of f^{5} and f^{2} equals f^{3}. Possible explanation: f * f * f * f * f / f * f = f * f * f / 1 = f^{3}. Cancel out the common f’s.

Below is the entire foldable with examples in a Word document. Each day you can add to the foldable and at the end of the lessons/unit, you will have notes for each area in one location. This attachment will be at the end of each lesson for Laws of Exponents.

(Foldables are interactive organizers created by Dinah Zike). This foldable is the Layered-Look Book.