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Exponents EQ: How can you evaluate negative exponents? Definition of an exponent An exponent tells how many times a number is multiplied by itself. 4 Base 4 3 Exponent 3 = (3)(3)(3)(3) = 81 How to read an exponent Three to the fourth power 4 3 How to read an exponent (cont’d) to the 2nd power or Three squared Three 2 3 How to read an exponent (cont’d) Three to the 3rd power or Three cubed 3 3 Exponents are often used in area problems to show the units are squared Area = (length)(width) 15ft Length = 30 ft Width = 15 ft 30ft 2 Area = (30 ft)(15 ft) = 450 ft A= 2 π(8cm) A = 64π 2 cm Exponents are often used in volume problems to show the units are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm 20 10 10 3 Volume = (20cm)(10cm)(10cm) = 2,000 cm What is the exponent? (5)(5)(5)(5) = 5 4 What is the answer? 5 3 = 125 What is the base and the exponent? (7)(7)(7)(7)(7) = 7 5 What is the base and the exponent? (x)(x)(x)(x)(x)(x) = x 6 What the base and the exponent? 3 2 (a)(a)(a)(b)(b)(c) = a b c Compute: 2 (-4) Answer: (-4)(-4) = 16 PEMDAS Calculate: 2 -4 Answer: -(4)(4) = -16 2 n when n = -5 2 (-5) = (-5)(-5) = 25 Simplify: Answer: Simplify: Answer: 2 -n 2 -(-5) when n = -5 = -(-5)(-5) = -25 Compute: 2 (-6) Answer: (-6)(-6) = 36 Compute: 2 -6 Answer: -(6)(6) = -36 Compute: 2 -(-6) Answer: -(-6)(-6) = -36 Simplify: (x + 2 3) Answer: (x + 3)(x + 3) 2 x + 6x + 9 Compute: 2 0 Answer: (0)(0) = 0 Compute: 0 2 Answer: 1 Yes, it’s 1…explanation will follow WHY is anything to the power zero "1" 6 3 = 729 35 = 243 4 3 = 81 3 3 = 27 32 = 9 1 3 =3 0 3 =1 Laws of Exponents 1. x 1 0 2. x 3. x x x m n m n 5. xy x y m m m x mn 7. n x x n 1 1 n n or n x x x 4. x m n m m x mn x x 6. m y y m A monomial is an algebraic expression consisting of only one term. A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –) Open Ended: Write 3 different examples of monomials Examples of monomials: 3, s, 3s, 3sp, 3s2p Determine whether each expression is a monomial. Say yes or no. Explain your reasoning. 1.) 10 1.) Yes, this is a constant, so it is a monomial. 2.) f + 24 2.) No, this expression has addition, so it has more than one term. 3.) 3ab5 3.) Yes, this expression is a product of a coefficient and variables. 4.) j 4.) Yes, single variables are monomials. Zero Exponent Property (1) Words: Any nonzero number raised to the zero power is equal to 1. Symbols: For any nonzero number a, a0 = 1. Examples: 1.) 120 = 1 0 2.) b 1 c 0 3.) 2 1 7 Open Ended: Create a problem that satisfies this property! Let’s practice Simplify each expression: 1. 2. 3. 4. 5. (-4)0 -40 (Recall PEMDAS - Exponents first!) (5x)0 5x0 -(-4.9)0 (Recall PEMDAS – Exponents first!) [(3x4y7z12)5 (–5x9y3z4)2]0 SWBAT… compute problems involving zero & negative exponents Wed, 4/6 Agenda 1. 2. 3. Review problems Zero & Negative Exponent Property (20 min) Practice – hw#1 (15 min) Quiz (10 min) WARM-UP 1. (5x)0 2. 5x0 3. Sophia ( Papaefthimiou ) 0 3 4. (2) HW: Quiz corrections Agenda 1. 2. 3. Lesson on monomials and exponents w/ many examples (20 min) Zero Exponent Property Negative Exponent Property Practice – hw#1 (15 min) Quiz (10 min) WARM-UP 1. (5x)0 2. 5x0 3.(Teacher)0 HW: workbook p.187 and 195 Negative Exponent Property (2) Words: For any nonzero number a and any integer n, a-n is the reciprocal of an. Also, the reciprocal of a-n = an. Symbols: For any nonzero number a and any integer n, a n 1 1 n n and n a a a Examples: 5 2 1 1 2 5 25 Open Ended: Create a problem that satisfies this property! Use any number for a and n. 1 3 m 3 m 12 8 1 4 Examples 1 12 1 1 4 4096 8 1 5 32 5 2 2 1 2 16 2 4 4 1 1 1 3 3 (2) ( 2 ) (2)( 2)( 2) 8 Examples (cont’d) 2 8 1 2 1 2 9(6) 9(1) 8 2 0 4 1 4 2 2 1 4 4 2 2 8 1 1 4 2 9 44 2 416 2 1 2 1 1 2 64 2 2 8 2 1 8 8 2 4 64 16 8 2 4 2 4 2 2 2 7 6 x y 0 2