Mastering Roots, Radicals, and Complex Numbers: A Complete Guide

1. Chapter 7 Roots, Radicals, and Complex Numbers

2. Chapter Sections 7.1 – Roots and Radicals 7.2 – Rational Exponents 7.3 – Simplifying Radicals 7.4 – Adding, Subtracting, and Multiplying Radicals 7.5 – Dividing Radicals 7.6 – Solving Radical Equations 7.7 – Complex Numbers

3. Rational Exponents § 7.2

4. When a is nonnegative, n can be any index. When a is negative, n must be odd. Changing a Radical Expression A radical expression can be written using exponents by using the following procedure:

5. For any nonnegative number a, and integers m and n, Power This rule can be expanded so that radicals of the form can be written as exponential expressions. Index Simplifying Radical Expressions

6. Simplify Radical Expressions Exponential form of For any nonnegative number a, Examples

7. For all real numbers a and b and all rational numbers m and n, Product rule:am •an = am + n Quotient rule: Negative exponent rule: Rules of Exponents The rules of exponents from Section 5.1 also apply when the exponents are rational numbers.

8. For all real numbers a and b and all rational numbers m and n, Zero exponent rule: a0 = 1, a 0 Raising a power to a power: Raising a product to a power : Raising a quotient to a power : Rules of Exponents

9. Rules of Exponents Examples: 1.) Evaluate 8-2/3. 2.) Evaluate

10. Rules of Exponents Examples Simplify each expression and write the answer without negative exponents. 1.) 2.)