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3/23/10 SWBAT… compute problems involving zero & negative exponents

3/23/10 SWBAT… compute problems involving zero & negative exponents . Agenda 1. Lesson on monomials and exponents (40 min) Zero Exponents Negative Exponents HW1: Zero and negative exponents. Monomials. Ms. Sophia Papaefthimiou Infinity HS.

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3/23/10 SWBAT… compute problems involving zero & negative exponents

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  1. 3/23/10SWBAT… compute problems involving zero & negative exponents Agenda 1. Lesson on monomials and exponents (40 min) • Zero Exponents • Negative Exponents HW1: Zero and negative exponents

  2. Monomials Ms. Sophia Papaefthimiou Infinity HS

  3. A monomial is a number, a variable or the product of a number and one or more variables with nonnegative integer exponents. • It has only one term. Examples of monomials: 3, s, 3s, 3sp • An expression that involves division by a variable, like is not a monomial.

  4. 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.) h2 3.) Yes, this expression is a product of variables. 4.) j 4.) Yes, single variables are monomials. 5.) 5.) No, this expression has a variable in the denominator.

  5. Definition of an exponent • An exponent tells how many times a number is multiplied by itself. 4 Exponent 3 Base 4 = (3)(3)(3)(3) 3

  6. How to read an exponent • This exponent is read three to the fourth power. 4 3

  7. How to read an exponent (cont’d) • This exponent is read three to the 2nd power or three squared. 2 3

  8. How to read an exponent (cont’d) • This exponent is read three to the 3rd power or three cubed. 3 3

  9. Exponents are often used in area problems to show the feet are squared Area = (length)(width) Length = 30 ft Width = 15 ft Area = (30 ft)(15 ft) = 450 ft 15ft 30ft 2

  10. Exponents are often used in volume problems to show the centimeters are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm Volume = (20cm)(10cm)(10cm) = 2,000 cm 20 10 10 3

  11. What is the exponent? 4 (5)(5)(5)(5) = 5

  12. What is the base and the exponent? 5 (7)(7)(7)(7)(7) = 7

  13. What is the answer? 3 5 125 =

  14. Compute: 02 Answer: 0

  15. Compute: (-4)2 Answer: (-4)(-4) = 16

  16. Compute: -42 Answer: -(4)(4) = -16

  17. Compute: 20 Answer: 1 Yes, it’s 1…explanation will follow

  18. Zero Exponent Property 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 2.) 3.)

  19. OYO Problems (On Your Own) Simplify each expression: 1.) (-4)0 2.) -40 3.) (-4.9)0 4. [(3x4y7z12)5 (–5x9y3z4)2]0

  20. WHY is anything to the power zero "1" • 35 = 36 ÷ 3 = 36 ÷ 31 = 36–1 = 35 = 243 • 34 = 35 ÷ 3 = 35 ÷ 31 = 35–1 = 34 = 81 • 33 = 34 ÷ 3 = 34 ÷ 31 = 34–1 = 33 = 27 • 32 = 33 ÷ 3 = 33 ÷ 31 = 33–1 = 32 = 9 • 31 = 32 ÷ 3 = 32 ÷ 31 = 32–1 = 31 = 3 • 30 = • 30 = 31 ÷ 3 = 31 ÷ 31 = 31–1 = 30 = 1

  21. Negative Exponent Property 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, Examples:

  22. OYO Problems (On Your Own)

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