1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-1 Basic Concepts Chapter 1

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Study Skills for Success in Mathematics, and Using a Calculator 1.2 – Sets and Other Basic Concepts 1.3 – Properties of and Operations with Real Numbers 1.4 – Order of Operations 1.5 – Exponents 1.6 – Scientific Notation Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-3 Exponents § 1.5

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-4 Exponents In the expression 3 4, the 3 is called the base, and the 4 is called the exponent. exponent 3434 base 3 4 is read “3 to the fourth power” and means 3·3·3·3 = 3 4 = 81 4 factors of 3 Note that x + x + x + x = 4x and x · x · x · x = x 4

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-5 -x 2 vs. (-x) 2 An exponent refers only to the number or letter that directly precedes it unless parentheses are used to indicate otherwise. – x 2 = – (x)(x) ( – x) 2 = (–x)(–x) = x 2 Example: –5 2 = –(5)(5) = –25 (–5) 2 = (–5)(–5) = 25

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-6 Product Rule for Exponents Example: Multiply each expression. a.) b.) c.)

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-7 Quotient Rule for Exponents Example: Divide each expression. b.) a.) c.)

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-8 Zero Exponent Rule a 0 = 1, x  0 Example: Simplify each expression. a.) b.) c.)

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-9 Negative Exponent Rule. Example: Write each expression without negative exponents. a.) b.) c.)

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-10 Power Rule for Exponents Example: Simplify each expression. a.) b.) c.)

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-11 Raising a Product to a Power Example: Simplify each expression. a.) b.)

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-12 Raising a Quotient to a Power Example: Simplify each expression. a.)