# Ch 11: Exponents and Exponential Expressions

### About This Chapter

## Exponents and Exponential Equations - Chapter Summary

The purpose of this chapter is to teach you how to work with positive and negative exponents, which typically appear as small, raised numbers to the left of a figure. Each lesson covers a specific topic and includes an online quiz that can help you decide if you're ready to progress to the next tutorial. Designed to help you pass the mathematical reasoning section of the GED exam, the chapter covers the following:

- The use of exponents in mathematics
- Scientific notations, including definition, examples and use
- Simplifying and solving exponential expressions
- Order of operations
- Multiplying and dividing exponential expressions
- The power of zero in simplifying exponential expressions
- Negative exponents, including how to write powers of fractions and decimals
- The power of powers and simplifying exponential expressions

Viewing and interactive activities are based upon easy-to-understand graphics and practice problems that are similar to those you'll find on the GED. When you've finished the chapter, you should have an understanding of exponential rules and know how to apply them to different mathematical expressions.

### GED Mathematical Reasoning Objectives

The GED is a 4-part test that reflects the Common Core State Standards as they apply to high school students in grades 9-12. The mathematical reasoning section is composed of two parts and must be completed in 90 minutes. Over half of this section, or 55%, consists of questions related to algebraic problem solving. The remaining 45% will test your understanding of quantitative reasoning principles and procedures. To help you avoid any surprises on exam day, lesson objectives include:

- How exponents relate to multiplication
- Writing numbers using scientific notation
- Writing exponential notations for products
- Using the order of operations to simplify an exponential expression
- Multiplying and dividing exponential expressions
- Raising a real number to the 0 power to simplify an exponential expression
- Writing powers of fractions or decimals using negative exponents
- Raising a power to a power to simplify an exponential equation

Successful completion of the exam will demonstrate your understanding of mathematical concepts and procedures, including their academic and real-life applications. The second portion of the exam requires the use of an on-screen scientific calculator, which will be provided.

### 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. Scientific Notation: Definition and Examples

Scientific notation is a special way of writing numbers so they are easier to work with. This lesson will define scientific notations and show some examples of how to convert numbers from standard notation to scientific notation and back.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. The Power of Zero: Simplifying Exponential Expressions

Raising a number to the power of zero is not the same as if the exponent is a number other than zero. This lesson will explain the rule involving using zero as an exponent and will give some examples of how it works.

### 8. Negative Exponents: Writing Powers of Fractions and Decimals

Most numbers can be written in different ways, either as a fraction, decimal or exponent. This lesson will teach you how to write fractions and decimals using exponents and how to convert between the two.

### 9. 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.

### 10. Exponential Form: Definition & Overview

Algebraic expressions written in exponential form are expressions written with an exponent. This lesson will define exponential form, give some examples, and follow with a quiz to test your understanding.

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### Other Chapters

Other chapters within the College Algebra: Help and Review course

- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Fractions
- Factoring
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Continuity in Mathematics
- Overview of Mathematical Limits