1. Section 1-2: Exponents and Order of Operations
Objectives: (1) To Simplify and evaluate formulas and expressions
(2) To add, subtract, multiply and divide expression with exponents
(3) To simplify and evaluate expressions with grouping symbols

2. Definitions
To simplify a numerical expression, you replace it with its simplest name.
An exponent tells how many times a number, the base, is used as a factor.
A power has two parts, a base and an exponent
You evaluate an algebraic expression by substituting a given number for each variable. Then Simplify the numerical expression using the order of operations.

3. Order of Operations Please, excuse my dear Aunt Sally. Please Excuse
Parenthesis ( ), or other grouping symbols like braces { } and brackets [ ]
Excuse
Exponents My
Multiplication
Dear
Division
Aunt
Addition
Sally
Subtraction

4. Order of Operations
This is the order in which you must begin evaluating expressions.
Multiplication and division are inverse operations (they undo each other) and therefore are done by the order in which they appear in the expression
Addition and subtraction are inverse operations and are done by the order in which they appear in the expression

5. Simplifying a Numerical Expression
Which operation appears 1st?
Exponents! Find 32
Now, multiplication
Subtraction comes first because add/subt is done by whichever comes first in the expression
And Add
18 is the simplified answer

6. Evaluating an Algebraic Expression
Evaluate 3a – 23 ÷ b a = 7 b = 4 3(7) – 23 ÷ (4) 3(7) – 8 ÷ 4 21 – 2 19
First replace all variables with their numerical counterparts with parenthesis
Exponents first
Multiplication AND Division
Subtraction
All Done

7. Real World Examples (Word Problems)
Your favorite pair of sneakers are on sale for $ There is a 6% sales tax in your state with any purchase. Find the total cost of the sneakers.
Use the following formula: C = p + r• p C is the cost P is the price R is the sales tax rate

8. Real World Examples (Word Problems)
C = 59 + (0.06)(59) C = C = You’re done!
Replace with actually values.
Order of operations tells us multiply first.
Now add
Easy, right?

9. Simplifying an Expression with Parenthesis
Simplify 15(13 – 7) ÷ (8 – 5) 15(6) ÷ (3) 90 ÷ 3 30 All done!
Simplify the stuff inside the parenthesis first.
Remember that no symbol between a number outside a parenthesis and the parenthesis means multiply
Now divide

10. Evaluating Expressions with Exponents
Evaluate each expression for c = 15 and d = 12
(cd)2
[(15)(12)]2
(180)2
32,400
Substitute 15 for c and 12 for d
Simplify the parenthesis first
Now raise it to the exponent

11. Evaluating Expressions with Exponents
Evaluate each expression for c = 15 and d = 12
cd2
(15)(12)2
(15)(144)
2,160
Substitute 15 for c and 12 for d
Raise 12 to the 2nd power first
Now multiply

12. Simplifying an Expression
Simplify 2[(13 – 7)2 ÷ 3] 2[(6)2 ÷ 3] 2[36 ÷ 3] 2 [ 12 ] 24 And you are done!
1st simplify the parenthesis
2nd Simplify the power
Simplify the brackets
Multiply

13. Real World Problem Solving: Urban Planning
A neighborhood association turned a vacant lot into a park. The park is shaped like the trapezoid to the right. Use the formula to find the area of the lot.
b1 = 100 ft
h = 130 ft
b2 = 200 ft

14. Real World Problem Solving: Urban Planning
We know: The area of the park is 19,500 ft2
Substitute 130 for h, 100 for b1 and 200 for b2
Simplify the numerator
Simplify the fraction
Multiply