# Ch 9: FTCE Middle Grades Math: Exponents & Exponential Expressions

### About This Chapter

## FTCE Middle Grades Math: Exponents & Exponential Expressions - Chapter Summary

This chapter takes an in-depth look at exponents and exponential expressions by exploring zero and negative exponents, the five main exponent properties, the order of operations and more. Make sure you fully understand these concepts, which will appear as exam topics on the FTCE Middle Grades Math assessment. By reviewing fun lessons, you will be able to:

- Explain how to use exponential notation, and identify and describe the five main exponent properties
- Define a zero and negative exponent, and describe exponents with fractional and decimal bases
- Describe how to go from a rational exponent to a radical expression and back and how to multiply with exponents
- Exhibit how to simplify expressions with exponents and simplify and solve exponential expressions
- Showcase your understanding of exponential expressions and the order of operations
- Demonstrate how to multiply and divide exponential expressions
- Share how to simplify expressions with rational exponents and simplify exponential expressions

All of the lessons in this chapter are available as videos or full transcripts with easily identifiable vocabulary words. Review them in any order you choose to improve your ability to answer questions related to exponents and exponential expressions on the exam. At any time, feel free to gauge your understanding of the subject area by taking the self-assessment quiz with each lesson. A chapter exam is also available to reinforce discussed learned in the lessons.

### 1. How to Use Exponential Notation

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

### 2. What Are the Five Main Exponent Properties?

We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!

### 3. How to Define a Zero and Negative Exponent

The zero and negative exponent properties are two you will use quite a lot in mathematics. The negative exponent property can be confusing, but when you remember a couple fun ideas, you will get it right every time!

### 4. Exponents with Fractional Bases

Watch this video lesson to learn how you can evaluate fractions that have exponents attached to them. Learn how the numerator and denominator behave with exponents.

### 5. Exponents with Decimal Bases

After watching this video lesson, you will be able to evaluate any exponents with decimal bases. Learn what the exponent does to the decimal and how to get your answer.

### 6. Rational Exponents

In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.

### 7. Multiplying With Exponents

Watch this video lesson to learn how you can use exponents to help you multiply numbers together. Learn what kinds of numbers you can multiply together with exponents and how to write them.

### 8. How to Simplify Expressions with Exponents

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

### 9. Simplifying and Solving Exponential Expressions

What do we do with an exponent? In this lesson, we'll learn how to simplify and solve expressions containing exponents. We'll solve a variety of types of exponential expressions.

### 10. Exponential Expressions & The Order of Operations

When performing mathematical operations, there is a specific order in which the operations should be performed. This includes when to simplify the exponents. This lesson will describe in what order exponents should be solved as you are performing mathematical operations.

### 11. Multiplying Exponential Expressions

There are certain rules that govern working with exponential expressions. This lesson deals with the rule for multiplying exponential expressions. It will describe the rule and give some examples of how it works.

### 12. Dividing Exponential Expressions

Any time you work with expressions that contain exponents, you have to follow a specific set of rules that are not the same as when you are working with expressions that do not contain exponents. This lesson will describe the rules associated with dividing terms that contain exponents.

### 13. Simplifying Expressions with Rational Exponents

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

### 14. Power of Powers: Simplifying Exponential Expressions

Mathematics is a very logical science. There is a rule for everything and not many exceptions to those rules. Working with exponents is no different. This lesson will describe the rule for raising a power to a power and also will give some examples in how to solve them.

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### Other Chapters

Other chapters within the FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide course

- About the FTCE Middle Grades Mathematics Test
- FTCE Middle Grades Math: Mathematical Reasoning
- FTCE Middle Grades Math: Problem-Solving Strategies
- FTCE Middle Grades Math: The Real Number System
- FTCE Middle Grades Math: Fractions, Decimals & Percents
- FTCE Middle Grades Math: Ratios & Proportions
- FTCE Middle Grades Math: Factoring
- FTCE Middle Grades Math: Solving Word Problems
- FTCE Middle Grades Math: Basic Algebraic Expressions
- FTCE Middle Grades Math: Distributing in Algebra
- FTCE Middle Grades Math: Rational Expressions
- FTCE Middle Grades Math: Square Roots
- FTCE Middle Grades Math: Radical Expressions
- FTCE Middle Grades Math: Linear Equations
- FTCE Middle Grades Math: Systems of Linear Equations
- FTCE Middle Grades Math: Solving & Graphing Inequalities
- FTCE Middle Grades Math: Introduction to Functions
- FTCE Middle Grades Math: Graphing Functions
- FTCE Middle Grades Math: Quadratic Functions
- FTCE Middle Grades Math: Polynomial Functions
- FTCE Middle Grades Math: Summarizing Data
- FTCE Middle Grades Math: Charting Data
- FTCE Middle Grades Math: Sampling
- FTCE Middle Grades Math: Probability Distributions
- FTCE Middle Grades Math: Lines & Angles
- FTCE Middle Grades Math: Properties of Triangles
- FTCE Middle Grades Math: Similar & Congruent Triangle Proofs
- FTCE Middle Grades Math: Right Triangle Proofs
- FTCE Middle Grades Math: Quadrilaterals & Polygons
- FTCE Middle Grades Math: Area & Perimeter
- FTCE Middle Grades Math: Circles & Arc of a Circle
- FTCE Middle Grades Math: Coordinate Geometry
- FTCE Middle Grades Math: Transformations in Geometry
- FTCE Middle Grades Math: Principles of Measurement
- FTCE Middle Grades Math: Surface Area & Volume
- FTCE Middle Grades Math: Connecting Math Concepts
- FTCE Middle Grades Math: Instructional Strategies & Tools
- FTCE Middle Grades Math: Assessing Student Learning
- FTCE Middle Grades Mathematics 5-9 Flashcards