# Ch 2: Exponents & Operations

### About This Chapter

## Exponents & Operations - Chapter Summary

Get the knowledge you need about exponents and operations by reviewing video lessons developed by expert instructors. Each lesson explores a unique topic to ensure you have a good grasp of the definitions and mathematical operations associated with exponents, square roots and scientific notation. Review the lessons at your leisure. In no time, you will be ready to:

- Go from rational exponents to radical expressions and back
- Identify the five main exponent properties
- Simplify expressions with exponents
- Add, subtract and multiply with exponents
- Divide exponential expressions
- Define zero and negative exponents
- Find the square root of a number, and estimate square roots
- Compare numbers written in scientific notation, and define its meaning

Watch the video lessons or access their full transcripts from your computer or mobile devices to get a quality understanding of exponents and operations. Lessons are accessible anytime, day or night, and can be revisited as many times as you'd like. Take the quiz with each lesson to test your knowledge of concepts covered. To get a more comprehensive review of the lessons, take the broader chapter exam.

### 1. Rational Exponents

Rational exponents are simply a fraction representing an exponent that is rewritten as a radical expression. Explore the concept of rational exponents and understand how they are converted to radical expressions through several example problems.

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

There are five main exponent properties, which are much like the order of operations in exponents, that give structure to simplifying expressions. Learn the formulas of the five exponent properties, including product of powers, power to a power, quotient of powers, power of a product, and power of a quotient.

### 3. How to Simplify Expressions with Exponents

Expressions can be rewritten using exponents to be simplified visually and mathematically. Explore the use of several properties used to simplify expressions with exponents, including the product of powers, power to a power, quotient of powers, power of a product, and the zero property.

### 4. Adding & Subtracting with Exponents

Exponents, or numbers raised to a power, can be easily added and subtracted by following a few rules to simplify the process. Learn the rules for adding and subtracting exponents, and practice the example problems, even when the exponent is '0'.

### 5. Multiplying With Exponents

Equations often contain exponents, the power that a number is raised to, that follow specific rules when multiplying. Learn how to multiply exponents, and see how the rules apply in two example problems.

### 6. Dividing Exponential Expressions

Dividing exponential expressions involves subtracting the exponents only when the base number of the terms is the same. Learn what an exponent is and the rules for dividing exponents with or without the same base number.

### 7. Zero Exponent: Rule, Definition & Examples

The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1. Explore the zero exponent rule, learn its definition, see examples, and solve an equation with zeros as exponents.

### 8. Negative Exponent: Definition & Rules

Negative exponents are written differently than positive exponents, though both are useful in avoiding writing out extremely large numbers. Learn more about the definition, rules, proper formatting of negative exponents.

### 9. How to Find the Square Root of a Number

Calculating the square root of a number is the inverse operation of squaring that number. Explore how to find square roots, the square of numbers, perfect and imperfect squares, and some square root practice examples.

### 10. Estimating Square Roots

Estimating square roots can be challenging, but it is one of the most common math operations. In this lesson, look at square roots, perfect square roots, the square roots of an imperfect square, estimating the square root, and example problems of all of these definitions.

### 11. Scientific Notation: Definition and Examples

Scientific Notation is the method of expressing very large or small numbers with exponents instead of a series of '0's. Discover how scientific notation is used, and examples to discern the difference in writing positive vs negative exponents.

### 12. Comparing Numbers Written in Scientific Notation

When numbers cannot be easily expressed as a decimal, they are written using scientific notation. Learn about comparing numbers written in scientific notation and review examples of numbers with scientific notation to recognize which is larger and which is smaller.

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### Other Chapters

Other chapters within the Pennsylvania Grades 4-8 - Math Subject Concentration (5158): Practice & Study Guide course

- Real & Rational Numbers
- Properties of Operations
- Fractions, Decimals & Percents
- Ratios, Rates & Proportional Relationships
- Number Theory & Estimation
- Radical & Exponential Expressions
- Linear Equations & Inequalities
- Nonlinear Equations & Inequalities
- Systems of Equations
- Sequences & Patterns in Math
- Understanding & Comparing Functions
- Function Graphs & Models
- Perimeter, Area & Volume Overview
- Properties of Angles & Lines
- Properties of Shapes Overview
- Geometric Relationships & Transformations
- Systems of Measurement & Conversion
- Geometric Construction
- Data Interpretation in Math
- Dispersion & Probability Models
- Logical Reasoning & Visual Representations of Data
- Pennsylvania Grades 4-8 - Math Subject Concentration (5158) Flashcards