Chapter 1 2 The Whole Numbers Copyright 2015

Chapter 1 2 The Whole Numbers Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 1

Section 1. 9 Exponents, Square Roots, and Order of Operations Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 2

Using Exponential Notation In the product 3 3 3, notice that 3 is a factor several times. The exponent, 5, indicates how many times the base, 3 is a factor. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 3

Using Exponential Notation Expression In Words 32 “three to the second power” or “three squared. ” 33 “three to the third power” or “three cubed” 34 “three to the fourth power” Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 4

Examples Write using exponential notation. 1. 2. 3. 4. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 5

Examples Evaluate. 1. 92 2. 45 3. 5 32 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 6

Evaluating Square Roots A square root of a number is one of two identical factors of the number. 7(7) = 49, so a square root of 49 is 7. We use the symbol (called a radical sign) for finding square roots. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 7

Examples Find each square root. a. = 10 because 10(10) = 100 b. = 2 because 2(2) = 4 c. = 1 because 1(1) = 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 8

Using the Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots, starting with the innermost set. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 9

Example Simplify: Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 10

Examples Simplify: Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 11

Example Simplify: Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 12

Example Simplify: Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 13

Example Simplify: Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 14

Finding the Area of a Square Example: Find the area of a square whose side measures 4 meters. Square 4 inches Area of a square = (side)2 = (4 inches)2 = 16 square inches Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 15