1.2 Exponents and Order of Operations

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1.2 Exponents and Order of Operations
2
Vocabulary

• Simplify
• Replace a numerical expression with its simplest
  name
• Is 32 5 simplified?
• Exponent
• Tells how many times you multiply the base by
  itself
• 32
• Base
• The number being multiplied in a given power
• 32
• Power
• The term for the base and exponent, combined
• 32

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Order of Operations

• P Parentheses or grouping symbols
• ( , ,
• E Exponents
• M Multiplication
• ?
• D Division
• ? , ? , /
• A Addition
• S Subtraction
• -

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1. Simplifying a Numerical Expression

• 25 7 ? 5 32
• 25 7 ? 5 9
• 25 35 9
• -10 9
• -1

P E M D A S

X
?
X
?
?
?
5
1. Simplifying a Numerical Expression

• b) 7 12 4
• -5 4
• -1

P E M D A S

X
X
X
X
?
?
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1. Simplifying a Numerical Expression

• c) 3 ? 4 ? 6
• 12 ? 6
• 2

P E M D A S

X
X
?
?
X
X
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2. Evaluating Algebraic Expressions

• a) 2x 17 3 where x2
• 2(2) 17 3
• Remember PEMDAS when simplifying
• 4 17 3
• 21 3
• 18
• d e u where d2, e1, and u17
• (2) (1) (17)
• Again, follow PEMDAS
• 3 17
• -14

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2. Evaluating Algebraic Expressions

• c) 40 d2 cd ? 3 where c2 and d 5
• 40 (5) 2 (2)(5) ? 3
• 40 25 (2)(5) ? 3
• 40 25 30
• 15 30
• 45

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3. Real World Application

• A poster states that a pair of shoes are on sale
  for 59.00. If the sales tax is 6, what is the
  total cost of the shoes?
• Use the formula c p rp
• C total cost
• P price of the shoes
• R sales tax rate
• C (59.00) (0.06)(59.00)
• C 59 3.54
• C 62.54
• The total cost of the shoes, including sales tax,
  will be 62.54.

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4. Simplifying More Expressions

• a) 15(12-6) ? (33)
• If it helps, make a PEMDAS box
• 15(6) ? (6)
• We now work from left to right
• 90 ? (6)
• 15
• b) (54) ? (7 3)
• If it helps, make a PEMDAS box
• (9) ? (4)
• 36

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5. Evaluate

• a) (xy)² where x3 and y4
• (3? 4)²
• Use PEMDAS to simplify
• 12²
• 144
• xy2 5 where y 5 and x 2
• 2(5) 2 5
• Use PEMDAS to simplify
• 2(25) 5
• 50 5
• 55

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5. Evaluate

• c) 2(x 1) (x)2 ? 8 where x 3
• 2(3 1) (3)2 ? 8
• Use PEMDAS to simplify
• 2(2) (3)2 ? 8
• 4 - (3)2 ? 8
• 4 9 ? 8
• 4 72
• -68

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Answers

• 59
• 22
• 7
• 113
• 32
• 29
• 21
• 27
• 124
• 15
• 180
• 169
• 16. 3
• 18. 5
• 20. 4
• 22. 7744
• 24. 361
• 26. 9
• 28. 3872