# Ch 5: High School Algebra: Exponents and Exponential Expressions

### About This Chapter

## Exponents and Exponential Expressions - Chapter Summary and Learning Objectives

Exponents are abbreviated notations that are used to indicate how many times a number or mathematical expression can be multiplied by itself. In a mathematical operation, they usually appear as a raised superscript to the right of a number and are referred to as powers. In this chapter, your instructor will show you how these shorthand notations can be used to write very large and small numbers that are too cumbersome or awkward to present in decimal form. You'll also learn the rules for simplifying and solving exponential expressions.

Each video in the series is devoted to a specific topic, such as the order of operations or the power of zero, and builds upon what you learned in the previous lesson. When you've finished the chapter and taken the online quizzes, you should be ready to:

- Write exponential notations
- Use the order of operations to solve exponential expressions
- Use the power of zero rule to solve exponential expressions
- Multiply and divide exponential expressions
- Use the power of powers rule to solve exponential expressions
- Use negative exponents to indicate powers of decimals or fractions

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

Working with Exponents | Explain how exponents relate to multiplication. Include special rules and examples in your discussion. |

Scientific Notation: Definition and Examples | Define scientific notation, including how it is used to write numbers. |

How to Use Exponential Notation | Explain how to write exponential notation for a product. Provide an example. |

Simplifying and Solving Exponential Expressions | Describe how to simplify and solve expressions in exponential notation. |

Exponential Expressions and the Order of Operations | Discuss how to simplify expressions using the rules for order of operations. |

Multiplying Exponential Expressions | Explain how to multiply an exponential equation. |

Dividing Exponential Expressions | Explain how to divide exponential expressions. |

The Power of Zero: Simplifying Exponential Expressions | Describe how to simplify exponential expressions using the rule for raising a real number to the 0 power to get 1. |

Negative Exponents: Writing Powers of Fractions and Decimals | Discuss how negative exponents can be used to write powers of fractions or decimals. |

Power of Powers: Simplifying Exponential Expressions | Explain how to simplify exponential expressions using the rule for raising a power to a power. |

### 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 I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability