Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 The Whole Numbers

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.9 Exponents, Square Roots, and Order of Operations

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation In the product 3  3  3  3  3, notice that 3 is a factor several times. The exponent, 5, indicates how many times the base, 3 is a factor.

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation ExpressionIn Words 3232 “three to the second power” or “three squared.” 3 “three to the third power” or “three cubed” 3434 “three to the fourth power”

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Evaluate = 9  9 = = 4  4  4  4  4 =  3 2 = 5  3  3 = 45

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating Square Roots A square root of a number is one of two identical factors of the number.

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Find each square root

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using the Order of Operations 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.

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify:

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify:

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify:

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Finding the Area of a Square Example: Find the area of a square whose side measures 4 meters. Square4 meters Area of a square = (side) 2 = (4 inches) 2 = 16 square meters