1. 1
Chapter
Chapter 2
The Whole Numbers

2. Exponents, Square Roots, and Order of Operations
Section
1.9
Exponents, Square Roots, and Order of Operations

3. Write Repeated Factors Using Exponential Notation.
Objective A
Write Repeated Factors Using Exponential Notation.

4. 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.

5. 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

6. Examples
Write using exponential notation. 1. 2. 3. 4.
Objective B

7. Evaluate Expressions Containing Exponents.
Objective B
Evaluate Expressions Containing Exponents.

8. Examples
Evaluate.
1. 92
2. 45
3. 5  32
Objective B

9. Evaluate the Square Root of a Perfect Square.
Objective C
Evaluate the Square Root of a Perfect Square.

10. 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.

11. Examples Find each square root. a. b. c. = 10 because 10(10) = 100

12. Use the Order of Operations.
Objective D
Use the Order of Operations.

13. 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

14. Example
Simplify:
Objective B

15. Examples
Simplify:
Simplify:

16. Example
Simplify:
Objective B

17. Example
Simplify:
Objective D Continued

18. Example
Simplify:

19. Find the Area of a Square.
Objective E
Find the Area of a Square.

20. 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