Chapter 7 Roots Radicals and Complex Numbers Copyright

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 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7 -2 2

§ 7. 2 Rational Exponents Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter

Changing a Radical Expression A radical expression can be written using exponents by using the following procedure: When a is nonnegative, n can be any index. When a is negative, n must be odd. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7 -4 4

Simplifying Radical Expressions This rule can be expanded so that radicals of the form can be written as exponential expressions. For any nonnegative number a, and integers m and n, Power Index Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7 -5 5

Simplify Radical Expressions Exponential form of For any nonnegative number a, Examples Copyright ©

Rules of Exponents The rules of exponents from Section 5. 1 also apply when the exponents are rational numbers. 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: Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7 -7 7

Rules of Exponents For all real numbers a and b and all rational numbers m and n, Zero exponent rule: a 0 = 1, a 0 Raising a power to a power: Raising a product to a power : Raising a quotient to a power : Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7 -8 8