# Ch 6: Exponential Expression Math

### About This Chapter

## Exponential Expression Math - Chapter Summary

This comprehensive overview of exponential expression math makes it easy for you to understand the many definitions and mathematical operations associated with exponents and expressions. Review these lessons at a pace that works for you until you feel confident that you've fully grasped these concepts. Once you've completed this chapter, you will be prepared for the following:

- Describing how to use exponential notation
- Identifying the five main exponent properties, and defining a zero and negative exponent
- Discussing exponents with fractional and decimal bases
- Showing how to go from a rational exponent to a radical expression and back
- Demonstrating how to simplify, solve, multiply and divide exponential expressions
- Exhibiting an ability to simplify expressions with exponents and multiply with exponents
- Sharing details about the order of operations and the power of powers

The lessons in this chapter are available in two formats. Watch them as videos with fun visual and audio effects, or read them as full transcripts with vocabulary words you can use to deepen your understanding of exponential expression math. With each lesson is a self-assessment quiz you can take to gauge your knowledge of concepts covered. If you answer a quiz question incorrectly, simply click the link next to the answer to revisit the related portion of the video lesson.

### 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 MEGA Mathematics: Practice & Study Guide course

- Number Theory & Basic Arithmetic
- Fractions, Decimals & Mixed Numbers
- Decimals
- Percents
- Ratios & Proportions
- Complex and Imaginary Numbers
- Vectors
- Matrix Operations
- Functions, Graphs & Properties
- Notation, Sequences & Series
- Linear Equation Properties
- Solving Systems of Linear Equations
- Graphing & Solving Inequalities
- Graphing and Factoring Quadratic Equations Overview
- Polynomial Functions Basics
- Higher-Degree Polynomial Functions
- Exponential Functions & Logarithmic Functions
- Rational Expressions and Function Graphs
- Radical Expressions
- Graphing Piecewise Functions
- Absolute Value Equations Review
- Principles of Measurement
- Area & Perimeter of Shapes
- Properties of 3D Figures in Math
- Fundamentals of Geometry Proofs
- Lines & Angles in Math
- Parallel Line Proofs in Geometry
- Triangle Properties
- Similar & Congruent Triangle Proofs in Geometry
- Right Triangles & Geometric Proofs
- Polygon Properties & Proofs
- Circles, Angles & Properties
- Conic Sections
- Applying Coordinate Geometry
- Geometric Transformations Overview
- Graph Symmetry Overview
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Overview of Continuity
- Understanding Rate of Change
- Limits
- Calculating Derivatives of Functions
- Understanding Graphing Derivatives & L'Hopital's Rule
- Understanding Applications of Derivatives
- Relationship Between Area Under the Curve & Integrals
- Indefinite Integrals in Calculus
- Interpreting Tables & Plots
- Data Summarization in Math
- Sampling & Statistical Bias
- Evaluating Probabilities
- Discrete Probability Distributions in Statistics
- Continuous Probability Distributions in Statistics
- MEGA Mathematics Flashcards