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MTH 11203 Algebra EXPONENTS, PARENTHESES, AND THE ORDER OF OPERATIONS CHAPTER 1 SECTION 9

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Learn the Meaning of Exponents General b n b is called the base, n is called the exponent n factors of b (b)(b)(b)(b)….(b) = b n b 4 = (b)(b)(b)(b) or bbbb x 3 = (x)(x)(x) or xxx

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Learning the Meaning of Exponents Whenever we see a variable or number without an exponent, we always assume that the exponent is 1 An exponent refers only to the number or variable that directly precedes it … unless parentheses are used to indicate otherwise. -x 2 not the same as (-x) 2 (-)(x)(x) (-x)(-x)

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Learn the Meaning of Exponents 3 2 3 is called the base, 2 is called the exponent 2 factors of 3 (3)(3) = 9 5 3 5 is called the base, 3 is called the exponent 3 factors of 5 (5)(5)(5) = 125

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#17 pg 77) 5 2 “5 squared” (5)(5)5 is the base, 2 is the exponent 25“5 to the second power” 2 factors of 5 #21 pg 777 3 “7 cubed” (7)(7)(7) “7 to the third power” (49)(7)3 factors of 7 3437 is the base, 3 is the exponent Exp:b 3 = b·b·b “b cubed” Exp:x 4 = x·x·x·x “x to the fourth” Expamples

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#28) 5 3 #19) 1 7 (5)(5)(5) (1)(1)(1)(1)(1)(1)(1) (25)(5)1 125 #20) 4 1 #37) (4) 4 Examples

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Write as an exponent: a) xyxx = x 3 y b) xyzzy = xy 2 z 2 c) 3aabb b = 3a 2 b 3 d) 5xyyyy = 5xy 3 e) (4)(4)rrs = 4 2 r 2 s f) (5)(5)(5)mmn = 5 3 m 2 n Exponential Notation

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Exponents refer to the number or variable directly preceding it unless it is in parenthesis EXP: -x 2 only the x will be squared (-)(x)(x) “negative x squared” or “the opposite of x squared” EXP: (-x) 2 all will be squared (-x)(-x) “negative x, quantity squared” EXP: -6 2 = (-)(6)(6) = -36 EXP: (-6) 2 = (-6)(-6)= 36 Difference between –x 2 and (-x) 2

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#30) (-7) 2 even neg. = pos. result (-7)(-7) -49 Exp) (-4) 4 even neg. = pos result (-4)(-4)(-4)(-4) (16)(-4)(-4) (-64)(-4) 256 Examples

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exp) -10 2 exp) (-10) 2 (-)(10)(10) (-10)(-10) -100100 exp) -4 3 exp)(-4) 3 odd neg. = neg. result (-)(4) (4)(4)(-4)(-4)(-4) -64(16)(-4) -64 Examples

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exp) (-3) 4 exp)-(3) 4 even neg. = pos. result (-3)(-3)(-3)(-3) (-)(3)(3)(3)(3) (9)(-3)(-3)(-3)(3)(3)(3) (-27)(-3)(-9)(3)(3) 81(-27)(3) -81 Examples

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EXP: (-5) 2 = (-5)(-5) = 25 EXP:-(5) 2 = -(5)(5) = -25 EXP:-2 3 = -(2)(2)(2) = -8 EXP:(-2) 3 = (-2)(-2)(-2) = -8 EXP:-2 4 = -(2)(2)(2)(2) = -16 EXP:(-2) 4 = (-2)(-2)(-2)(-2) = 16 EXP:(-7) 2 = (-7)(-7) = 49 EXP:(-3) 3 = (-3)(-3)(-3) = -27 Difference between –x 2 and (-x) 2

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Help using your calculator is on page 70 EXP:-10 2 = -(10)(10) = -100 EXP:(-10) 2 = (-10)(-10) = 100 EXP:-4 3 = -(4)(4)(4) = -64 EXP:(-4) 3 = (-4)(-4)(-4) = -64 Calculator

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Order of Operation 1. Evaluate within grouping symbols { }, [ ], ( ) innermost parenthesis first 2. Evaluate exponents 3. Multiply or Divide from left to right 4. Add or Subtract from left to right Please Excuse My Dear Aunt Sally – PEMDAS Remember its multiply or divide, add or subtract Parenthesis can be used to change the order of operations or to clarify the order EXP: 2 + 3 · 4 = 2 + (3 · 4) = 2 + 12 = 14 Learning the Order of Operations

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Nested Parenthesis is one set inside another Use the innermost parenthesis first. EXP:EXP: Learning the Order of Operations

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EXP:EXP: Examples

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EXP:EXP: Examples

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EXP:EXP: Examples

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EXP: Examples

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Write the following statement as mathematical expressions using parentheses and brackets and then evaluate. Multiply 9 by 6, add 7 to this product. Subtract 12 from the sum. Divide this difference by 5. [[(9 * 6) + 7] – 12] ÷ 5 49/5

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EXP: Evaluate Expressions Containing Variables

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EXP: Evaluate Expressions Containing Variables

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EXP: Evaluate Expressions Containing Variables

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EXP: Evaluate Expressions Containing Variables

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HOMEWORK 1.9 Page 77 – 78 #18, 21, 29, 35, 43, 57, 61, 75, 79, 83, 87, 95

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