# Ch 15: Exponentiation & Rational Numbers

### About This Chapter

## Exponentiation & Rational Numbers- Chapter Summary

A frequent exercise in mathematics is solving equations based on rational numbers and expressions. Further, the application of exponentiation is very important in mathematics. This chapter explains all the algebra involved in solving mathematical equations involving rational numbers along with the application of exponentiation. The topics covered in the chapter are listed below:

- Exponential function
- Logarithm and its application
- Solving a rational equation
- Performing addition/subtraction in rational expressions
- Performing multiplication/division in rational expressions
- Absolute value and its use
- Solving radical equation

The chapter is thoughtfully prepared by our experts to give you a complete understanding and expertise in the mathematics of rational numbers and exponentiation. There are short videos given on the topics to make it more interesting. You can review the topic, pause, and resume it at your convenience. You can check your knowledge easily by answering the quizzes provided at the end of each lesson.

The dashboard provides you with links to each lesson and helps you to track your progress through the chapter.

### 1. What Is an Exponential Function?

Exponential functions have a constant base with an independent variable that is an exponent, such as y = ab^x. Learn more about functions with exponents and find two examples that demonstrate the way exponential functions appear on graphs.

### 2. Exponential Growth vs. Decay

Exponential growth and decay are the results of a continuous pattern of numbers found in exponential fractions. Learn more about the differences between exponential growth and exponential decay, and learn how to solve more complex problems by determining a starting value.

### 3. What is a Logarithm?

Using logarithms is simply a different way of evaluating exponential expressions. Discover how exponents work together with logarithms and learn what logarithm notation looks like and how to use it by solving example problems.

### 4. How to Solve a Rational Equation

Solving a rational equation involves finding the common denominator and multiplying all numbers by it, then simplifying and checking the answer. Explore rational equations and apply the steps involved to solve example problems.

### 5. How to Add and Subtract Rational Expressions

Rational polynomial expressions are fractions with a numerator and denominator that are polynomials and can be simplified as needed and act similarly to fractions when identifying a common denominator. Learn how rational expressions are added and subtracted by simplifying through several steps demonstrated in examples.

### 6. How to Multiply and Divide Rational Expressions

Polynomial retinal expressions, being a fraction that contains a polynomial, are able to be divided and multiplied similarly to normal fractions. Explore the extra steps involved through three examples of how to factor, flip, slash, and multiply and divide rational expressions when needed.

### 7. What is an Absolute Value?

Absolute value in mathematics involves focusing on the size of a number instead of its sign. Explore the distance from zero, notation of absolute values, and solving equations with absolute values.

### 8. How to Evaluate Absolute Value Expressions

An absolute value expression can be evaluated, but all operations contained within the absolute value bars must be completed before making it positive. Learn how to solve an absolute value expression by substituting individual variables and replacing groups of variables.

### 9. How to Solve an Absolute Value Equation

An absolute value equation includes a variable that is an absolute value as one of the variables resulting in two solutions, the positive or negative. Learn about the methods of solving basic absolute value equations and why it is necessary to split an absolute value equation into two possible equations to solve for the variable.

### 10. 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.

### 11. Radicands and Radical Expressions

Radical expressions refer to expressions that include radicals, or square root signs. Explore the definition of a radical symbol and radicand, and understand the rules for radical expressions, including why they only work with real numbers.

### 12. Solving Radical Equations: Steps and Examples

A radical equation is an equation in which a variable is under a radical. Learn to identify radicals, perform inverse operations, and solve radical equations through real-world examples.

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### Other Chapters

Other chapters within the NES Essential Academic Skills Mathematics Subtest 3 (003): Practice & Study Guide course

- About the NES Test
- NES Essential Academic Skills Math: Decimals
- NES Essential Academic Skills Math: Fractions
- NES Essential Academic Skills Math: Estimating & Rounding
- NES Essential Academic Skills Math: Percent Notation
- NES Essential Academic Skills Math: Computing Integers
- NES Essential Academic Skills Math: Rates & Ratios
- Understanding Mathematical Problems
- Types of Numbers & Number Theory
- Basics of Numerical Functions
- NES Essential Academic Skills Math: Linear Equations
- NES Essential Academic Skills Math: Graphing Functions
- NES Essential Academic Skills Math: Quadratic Equations
- NES Essential Academic Skills Math: Inequalities
- NES Essential Academic Skills Math: Piecewise Functions
- NES Essential Academic Skills Math: Measurement
- NES Essential Academic Skills Math: Perimeter & Area
- NES Essential Academic Skills Math: Geometric Figures
- NES Essential Academic Skills Math: Types of Angles
- NES Essential Academic Skills Math: Triangles
- NES Essential Academic Skills Math: Quadrilaterals
- NES Essential Academic Skills Math: Circles & Arcs
- NES Essential Academic Skills Math: 3D Shapes & Geometric Solids
- Geometric Transformation & Symmetry
- NES Essential Academic Skills Math: Triangle Theorems & Proofs
- NES Essential Academic Skills Math: Similar Polygons
- NES Essential Academic Skills Math: The Pythagorean Theorem
- NES Essential Academic Skills Math: Graphing Coordinates
- NES Essential Academic Skills Math: Trigonometric Functions
- NES Essential Academic Skills Math: Continuity
- Understanding Statistics
- NES Essential Academic Skills Math: Probability
- NES Essential Academic Skills Math: Discrete Math
- NES Essential Academic Skills Mathematics Subtest 3 Flashcards