Exponents, Parentheses, and the Order of Operations MTH 11203 Algebra Exponents, Parentheses, and the Order of Operations CHAPTER 1 Section 9

Learn the Meaning of Exponents General bn b is called the base, n is called the exponent n factors of b (b)(b)(b)(b)….(b) = bn b4 = (b)(b)(b)(b) or bbbb x3 = (x)(x)(x) or xxx

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. -x2 not the same as (-x)2 (-)(x)(x) (-x)(-x)

Learn the Meaning of Exponents 32 3 is called the base, 2 is called the exponent 2 factors of 3 (3)(3) = 9 53 5 is called the base, 3 is called the exponent 3 factors of 5 (5)(5)(5) = 125

Expamples #17 pg 77) 52 “5 squared” (5)(5) 5 is the base, 2 is the exponent 25 “5 to the second power” 2 factors of 5 #21 pg 77 73 “7 cubed” (7)(7)(7) “7 to the third power” (49)(7) 3 factors of 7 343 7 is the base, 3 is the exponent Exp: b3 = b·b·b “b cubed” Exp: x4 = x·x·x·x “x to the fourth”

Examples #28) 53 #19) 17 (5)(5)(5) (1)(1)(1)(1)(1)(1)(1) (25)(5) 1 125 #20) 41 #37) (4) 4

Exponential Notation Write as an exponent: xyxx = x3y xyzzy = xy2z2 3aabb b = 3a2b3 5xyyyy = 5xy3 (4)(4)rrs = 42r2s (5)(5)(5)mmn = 53m2n

Difference between –x2 and (-x)2 Exponents refer to the number or variable directly preceding it unless it is in parenthesis EXP: -x2 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: -62 = (-)(6)(6) = -36 EXP: (-6)2 = (-6)(-6)= 36

Examples #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 exp) -102 exp) (-10)2 (-)(10)(10) (-10)(-10) -100 100 exp) -43 exp) (-4)3 odd neg. = neg. result (-)(4) (4)(4) (-4)(-4)(-4) -64 (16)(-4) -64

Examples 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

Difference between –x2 and (-x)2 EXP: (-5)2 = (-5)(-5) = 25 EXP: -(5)2 = -(5)(5) = -25 EXP: -23 = -(2)(2)(2) = -8 EXP: (-2)3 = (-2)(-2)(-2) = -8 EXP: -24 = -(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

Calculator Help using your calculator is on page 70 EXP: -102 = -(10)(10) = -100 EXP: (-10)2 = (-10)(-10) = 100 EXP: -43 = -(4)(4)(4) = -64 EXP: (-4)3 = (-4)(-4)(-4) = -64

Learning the Order of Operations Evaluate within grouping symbols { }, [ ], ( ) innermost parenthesis first Evaluate exponents Multiply or Divide from left to right 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 Nested Parenthesis is one set inside another Use the innermost parenthesis first. EXP: EXP:

Examples EXP: EXP:

Examples EXP: EXP:

Examples EXP: EXP:

Examples EXP:

Examples 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

Evaluate Expressions Containing Variables

Evaluate Expressions Containing Variables

Evaluate Expressions Containing Variables

Evaluate Expressions Containing Variables

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