# Ch 13: Calculating & Simplifying Exponential Expressions

### About This Chapter

## Calculating & Simplifying Exponential Expressions - Chapter Summary and Learning Objectives

You can begin this study by reviewing examples and usage of exponential notation. Then you'll practice simplifying, calculating and solving exponential expressions, focusing on the order of operations, the power of zero, negative exponents and power of powers. By the time you've wrapped up this chapter, you'll be confident in working with the following:

- The order of operations related to exponential expressions
- Strategies for multiplying and dividing exponential expressions
- Methods for simplifying exponential expressions
- How to write powers of fractions and decimals

Video | Objective |
---|---|

How to Use Exponential Notation | Examine the strategies for working with exponential notation. |

Scientific Notation: Definition and Examples | Look over helpful examples of scientific notation. |

Simplifying and Solving Exponential Expressions | Follow the instructor's steps for simplifying and then solving exponential expressions. |

Exponential Expressions & The Order of Operations | Review the order of operations and learn how that affects exponential expressions. |

Multiplying Exponential Expressions | Practice strategies for the multiplication of exponential expressions. |

Dividing Exponential Expressions | Explore the essentials for dividing exponential expressions and find how that relates to multiplication. |

The Power of Zero: Simplifying Exponential Expressions | Discover the power of zero and the relationship to simplification of exponential expressions. |

Negative Exponents: Writing Powers of Fractions and Decimals | Find out the key steps in writing powers of decimals and fractions. |

Power of Powers: Simplifying Exponential Expressions | Use basic knowledge related to power of powers to simplify exponential expressions. |

### 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.

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### Other Chapters

Other chapters within the Algebra 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs