Section 1-2 Exponents and Order of Operations SPI 11E: Apply order of operations when computing with integers SPI 12E: Use estimation to determine a reasonable solution Objectives: Simplify and evaluate expressions and formulas Vocabulary Simplify Replace an expression or equation with its simplest name Evaluate Substitute a given number for a variable Example: Simplify The answer is 8. Example: Evaluate 3a – 2 for a = 7. Answer: 3(7) – 2 = 21 – 2 = 19

1. Parenthesis and Brackets (grouping) 2. Exponents (Powers) 3. Multiplication and Division (Left to right) 4. Addition and Subtraction (Left to right) Why is it necessary to have order of operations? Use to avoid having two different results – 6 ÷ 2 = 8 – 6 ÷ 2 = 2 ÷ 2 = – 6 ÷ 2 = – 3 = 8 – 3 = 5 Review Order of Operation

a. 6 – 10 ÷ 5 b ÷ 2 c. 3(8 + 6) ÷ (52 – 10) d. 4[(2 9) + (15 ÷ 3)2] Practice using Order of Operations

Substitute a given number for a variable Evaluate 3a for a = 2. Answer: 3(2) = 6 Steps for Evaluating an Algebraic Expression 1. Rewrite expression substituting values for variables. (Put values in parenthesis to avoid error) 2. Simplify using the order of operation Evaluate 3a – 24 ÷ b, for a=7, b=4 3a – 24 ÷ b =3(7) – 24 ÷ (4) = 21 – 6 = 15 Evaluate an Algebraic Expression Rewrite substituting variable Simplify using PEMDAS

Exponents Shorthand way to show products of like factors Shows how many times a base is used as a factor Power: has a base and exponent = 2 3 Exponent Factors Base 2 3 is read as “2 to the third power” or “2 cubed”

Exponent Examples 1. Write in exponent form: = 2. Write in expanded form then simplify: Simplify Simplify Write in expanded form then simplify: 2 1 ∙ ∙ 5 ∙ 5 = = 2 ∙ 3 ∙ 3 ∙ 3 = 54

a. (cd) 2 b. cd 2 c. c 0 d 2 d. 2cd 2 Practice Evaluating Expressions with Exponents (15 ∙ 12) 2 = (180) 2 = 32, (12) 2 = 15(144) = 2,160 (15) 0 ∙ (12) 2 = 1 (144) = (15) (12) 2 = 30(144) = 4,320 Evaluate each expression for c = 15 and d = 12.

Use the formula for speed to solve the following problems. Speed = distance time 1. A car has traveled 460 miles in 8 hours. What is the average speed traveled? 2. If the speed limit is 60 mph, did the car exceed the speed limit? Speed = = 57.5 mph NOPE Relate Evaluating Expressions to Physical Science

State sales tax 6% Solve a Real-World Problem Shoe Emporium is having a sale on sneakers. You have $62 in cash. Write an equation for this problem. Do you have enough money to buy the shoes? Find the total cost of the sneakers shown by using the formula below. Cost = original price+ sales tax rate C = p + (r ∙ p) C = 59 + (0.06)(59) = = 62.54