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

Slide 2 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Exponents, Square Roots, and Order of Operations Section1.9

Slide 3 Copyright © 2015, 2011, 2008 Pearson Education, Inc. 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.

Slide 4 Copyright © 2015, 2011, 2008 Pearson Education, Inc. 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”

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

Slide 6 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Examples Evaluate  3 2

Slide 7 Copyright © 2015, 2011, 2008 Pearson Education, Inc. 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.

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

Slide 9 Copyright © 2015, 2011, 2008 Pearson Education, Inc. 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.

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

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

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

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

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

Slide 15 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Finding the Area of a Square Example: Find the area of a square whose side measures 4 meters. Square4 inches Area of a square = (side) 2 = (4 inches) 2 = 16 square inches