1 Chapter Chapter 2 The Whole Numbers
Exponents, Square Roots, and Order of Operations Section 1.9 Exponents, Square Roots, and Order of Operations
Write Repeated Factors Using Exponential Notation. Objective A Write Repeated Factors Using Exponential Notation.
Using Exponential Notation In the product 3 3 3 3 3, notice that 3 is a factor several times. Objective A The exponent, 5, indicates how many times the base, 3 is a factor.
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” Objective A Continued
Examples Write using exponential notation. 1. 2. 3. 4. Objective B
Evaluate Expressions Containing Exponents. Objective B Evaluate Expressions Containing Exponents.
Examples Evaluate. 1. 92 2. 45 3. 5 32 Objective B
Evaluate the Square Root of a Perfect Square. Objective C Evaluate the Square Root of a Perfect Square.
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.
Examples Find each square root. a. b. c. = 10 because 10(10) = 100
Use the Order of Operations. Objective D Use the Order of Operations.
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. Objective D
Example Simplify: Objective B
Examples Simplify: Simplify:
Example Simplify: Objective B
Example Simplify: Objective D Continued
Example Simplify:
Find the Area of a Square. Objective E Find the Area of a Square.
Finding the Area of a Square Example: Find the area of a square whose side measures 6 meters. Square 6 inches Area of a square = (side)2 = (6 inches)2 = 36 square inches Objective E