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Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
Properties Of Exponents
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Properties Of Exponents

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  • 1. Properties of Exponents p. 323
  • 2. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Product Property : </li></ul><ul><li>Quotient of Powers : </li></ul><ul><li>Power of a Power Property : </li></ul><ul><li>Power of a Product Property : </li></ul><ul><li>Negative Exponent Property : </li></ul><ul><li>Zero Exponent Property : </li></ul><ul><li>Power of Quotient: </li></ul>
  • 3. Example – Product Property <ul><li>(-5) 3 (-5) 2 = </li></ul><ul><li>(-5)(-5)(-5)(-5)(-5)= </li></ul><ul><li>(-5) 5 </li></ul><ul><li>(-5) 3+2 = </li></ul><ul><li>(-5) 5 </li></ul>
  • 4. Example – Product Property <ul><li>x 5 • x 2 = x •x• x •x•x•x•x </li></ul><ul><li>x 5+2 = </li></ul><ul><li>x 7 </li></ul>
  • 5. Product Property a&b are real numbers, m&n are integers <ul><li>Product Property : (a m )(a n )=a m+n </li></ul><ul><li>a 3 • a 5 • a 4 = </li></ul><ul><li>a 3 • a 5 • a 4 = a 3+5+4 </li></ul><ul><li>a 3 • a 5 • a 4 = a 12 </li></ul>
  • 6. Product Property <ul><li>(a 3 b 2 ) (a 4 b 6 ) = </li></ul><ul><li>(a 3 a 4 ) (b 2 b 6 ) = a 3+4 b 2+6 </li></ul><ul><li>a 3+4 b 2+6 = a 7 b 8 </li></ul><ul><li>(x 5 y 2 ) (x 4 y 7 ) = </li></ul><ul><li>(x 5 x 4 ) (y 2 y 7 ) = x 5+4 y 2+7 </li></ul><ul><li>x 5+2 y 2+7 = x 9 y 9 </li></ul>
  • 7. You try <ul><li>(3x 6 y 4 ) (4xy 7 ) = </li></ul><ul><li>(3x 6 y 4 ) (4xy 7 ) = (3 •4) x 6+1 • y 4+7 </li></ul><ul><li>(3 •4) x 6+1 • y 4+7 = 12x 7 y 11 </li></ul><ul><li>(2x 12 y 5 ) (6x 3 y 9 ) = </li></ul><ul><li>(2 • 6) x 12+3 y 5+9 =12x 15 y 14 </li></ul>
  • 8. Do now <ul><li>(2x 4 y 4 ) (5xy 7 ) = </li></ul><ul><li>(2x 4 y 4 ) (5xy 7 ) = (2 •5) x 4+1 • y 4+7 </li></ul><ul><li>(2 •5) x 4+1 • y 4+7 = 10x 5 y 11 </li></ul><ul><li>(3x 14 y 5 ) (9x 3 y) = </li></ul><ul><li>(3 • 9) x 14+3 y 5+1 =27x 17 y 6 </li></ul>
  • 9. Dividing Powers with Like bases <ul><li>-5 3 = -5 • -5 • -5 </li></ul><ul><ul><li>-5 2 -5 • -5 </li></ul></ul><ul><li>-5 • -5 • -5 = -5 </li></ul><ul><li>-5 • -5 </li></ul>
  • 10. Power of a Quotient with like bases <ul><li>x 4 = x • x • x • x </li></ul><ul><li>X 2 x • x </li></ul><ul><li>X 2 </li></ul>
  • 11. Quotient of Powers
  • 12. Quotient of Powers <ul><li>Quotient of Powers : </li></ul><ul><li>a m = a m-n ; a≠0 </li></ul><ul><li>a n </li></ul>
  • 13. You try <ul><li>4 5 x 4 y 7 = </li></ul><ul><li>4 3 x 2 y 6 </li></ul><ul><li>4 5 x 4 y 7 = 4 5-3 x 4-2 y 7-6 </li></ul><ul><li>4 3 x 2 y 6 </li></ul><ul><li>4 5-3 x 4-2 y 7-6 = 4 2 x 2 y = 16x 2 y </li></ul>
  • 14. You try <ul><li>3 7 x 9 y 12 = </li></ul><ul><li>3 4 x 5 y 6 </li></ul><ul><li>3 7 x 9 y 12 = 3 7-4 x 9-5 y 12-6 </li></ul><ul><li>3 4 x 5 y 6 </li></ul><ul><li>3 7-4 x 9-5 y 12-6 = 3 3 x 4 y 8 = 27x 4 y 8 </li></ul>
  • 15. Negative Exponents <ul><li>x 2 = x • x_____ </li></ul><ul><li>x 4 x • x • x • x </li></ul><ul><li>1 = </li></ul><ul><li>x 2 </li></ul><ul><li>x 2 = x 2 -4 = x -2 </li></ul><ul><li>X 4 </li></ul><ul><li>x -2 = 1 </li></ul><ul><li>x 2 </li></ul>
  • 16. Negative exponets <ul><li>x 3 = x • x_ • x___ </li></ul><ul><li>x 5 x • x • x • x • x </li></ul><ul><li>1 = </li></ul><ul><li>x 3 </li></ul><ul><li>x 3 = x 3 -5 = x -3 </li></ul><ul><li>x 5 </li></ul><ul><li>x -3 = 1 </li></ul><ul><li>x 3 </li></ul>
  • 17. Example – Quotient of Powers
  • 18. You try <ul><li>x -2 = </li></ul><ul><li>1 </li></ul><ul><li>x 2 </li></ul><ul><li>2x -2 y = </li></ul><ul><li>2x -2 y = 2y </li></ul><ul><li>x 2 </li></ul>
  • 19. You try <ul><li>(-5) -6 (-5) 4 = </li></ul><ul><li>(-5) -6+4 = </li></ul><ul><li>(-5) -2 = </li></ul>
  • 20. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Negative Exponent Property : </li></ul><ul><li>a -m = ; a ≠0 </li></ul>
  • 21. Zero Exponent Property <ul><li>x 0 </li></ul><ul><li>x 2 = x 2-2 </li></ul><ul><li>x 2 </li></ul><ul><li>x 2-2 = x 0 </li></ul><ul><li>x 2 = 1 </li></ul><ul><li>x 2 </li></ul><ul><li>x 0 = 1 </li></ul>
  • 22. You try <ul><li>(x -2 ) (x 2 ) = </li></ul><ul><li>(x -2 ) (x 2 ) = x -2+2 </li></ul><ul><li>x -2+2 = x 0 </li></ul><ul><li>x 0 = 1 </li></ul>
  • 23. Properties of Exponents a&b are real numbers, m&n are integers ets Review <ul><li>Zero Exponent Property : a 0 =1; a≠0 </li></ul>
  • 24. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Product Property : a m * a n =a m+n </li></ul><ul><li>Quotient of Powers : a m = a m-n ; a≠0 a n </li></ul><ul><li>Negative Exponent Property : a -m = ; a ≠0 </li></ul><ul><li>Zero Exponent Property : a 0 =1; a≠0 </li></ul>
  • 25. Journal Entry: Describe the rules for the follwoing <ul><li>Product Property : </li></ul><ul><li>Quotient of Powers : </li></ul><ul><li>Negative Exponent Property : </li></ul><ul><li>Zero Exponent Property : </li></ul>
  • 26. Example – Power of a Power <ul><li>(2 3 ) 4 = (2 3 ) (2 3 ) (2 3 ) (2 3 ) 4 </li></ul><ul><li>2 3+3+3+3 = </li></ul><ul><li>(2 3 ) 4 = 2 12 </li></ul>
  • 27. Example - Power of a Power <ul><li>(3 4 ) 3 = (3 4 ) (3 4 ) (3 4 ) </li></ul><ul><li>(3 4 ) (3 4 ) (3 4 ) = 3 4+4+4 </li></ul><ul><li>(3 4 ) 3 = 3 12 </li></ul>
  • 28. Raising a Power to a Power <ul><li>(X 5 ) 2 = (X 5 ) (X 5 ) </li></ul><ul><li>(X 5 ) (X 5 )= x 5+5 </li></ul><ul><li>(X 5 ) 2 = x 10 </li></ul>
  • 29. Power of a Power Property a&b are real numbers, m&n are integers <ul><li>Power of a Power Property : (a m ) n =a mn </li></ul><ul><li>(x 5 ) 3 = x 5 • 3 </li></ul><ul><li>x 5 • 3 = x 15 </li></ul>
  • 30. You try <ul><li>(y 4 ) 8 = </li></ul><ul><li>(y 4 ) 8 = y 4 •8 = y 24 </li></ul><ul><li>(s 3 ) 4 = </li></ul><ul><li>(s 3 ) 4 = s 3 •4 = s 12 </li></ul>
  • 31. Power of a Product Property <ul><li>(-2x 7 ) 2 = (-2x 7 ) (-2x 7 ) </li></ul><ul><li>(-2x 7 ) (-2x 7 ) = (-2 • - 2) (x 7 • x 7 ) =4x 14 </li></ul><ul><li>(-2x 7 ) 2 = (-2) 2 (x 7 ) 2 = -2 1 •2 x 7 • 2 </li></ul><ul><li>= 4x 14 </li></ul>
  • 32. <ul><li>Power of a Product Property : (ab) m =a m b m </li></ul><ul><li>(a 3 b 2 ) 4 = (a 3 ) 4 (b 2 ) 4 </li></ul><ul><li>(a 3 ) 4 (b 2 ) 4 = a 3 •4 b 2 •4 =a 12 b 8 </li></ul>
  • 33. You try <ul><li>(-2x 4 ) 3 = (-2) 1 • 3 x 5 • 3 </li></ul><ul><li>(-2x 4 ) 3 = (-2) 1 • 3 x 4 • 3 </li></ul><ul><li>(-2) 1 • 3 x 4 • 3 = (-2) 3 x 12 = -16x 12 </li></ul><ul><li>(4x 4 y 5 ) 2 </li></ul><ul><li>(4x 4 y 5 ) 2 = 4 1 • 2 x 4 • 2 y 5 • 2 </li></ul><ul><li>(4x 4 y 5 ) 2 = 16x 8 y 10 </li></ul>
  • 34. You try <ul><li>(-3x 5 y 3 ) 4 = </li></ul><ul><li>(-3) 1 • 4 x 5 • 4 y 4 • 4 = (-3) 4 x 20 y 16 </li></ul><ul><li>(7x 3 y -5 ) 2 </li></ul><ul><li>7 1 • 2 x 3 • 2 y -5 • 2 </li></ul><ul><li>16x 8 y -10 = 16x 8 </li></ul><ul><li>y 10 </li></ul>
  • 35. Example – Power of Quotient
  • 36. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Power of Quotient: </li></ul><ul><li>b≠0 </li></ul>
  • 37. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Product Property : a m * a n =a m+n </li></ul><ul><li>Quotient of Powers : a m = a m-n ; a≠0 a n </li></ul><ul><li>Power of a Power Property : (a m ) n =a mn </li></ul><ul><li>Power of a Product Property : (ab) m =a m b m </li></ul><ul><li>Negative Exponent Property : a -m = ; a ≠0 </li></ul><ul><li>Zero Exponent Property : a 0 =1; a≠0 </li></ul><ul><li>Power of Quotient: b≠0 </li></ul>
  • 38. Multiplying and Dividing Monomials <ul><li>Monomial – an expression that is either a numeral, a variable or a product of numerals and variables with whole number exponents. </li></ul><ul><li>Constant – Monomial that is a numeral. Example - 2 </li></ul>
  • 39. Journal Entry: Describe the rules for the follwoing <ul><li>Power of a Power Property : </li></ul><ul><li>Power of a Product Property : </li></ul><ul><li>Power of Quotient: </li></ul>
  • 40. Multiplying Monomials <ul><li>(-2x 4 y 2 ) (-3xy 2 z 3 ) = </li></ul><ul><li>(-2)(-3)(x 4 x )(y 2 y 2 ) z 3 </li></ul><ul><li>6x 5 y 4 z 3 </li></ul><ul><li>(-2x 3 y 4 ) 2 (-3xy 2 ) </li></ul><ul><li>(-2 ) 2 x 3∙2 y 4∙2 ) (-3xy 2 ) </li></ul><ul><li>(4)(-3)(x 6 x) (y 8 y 2 ) </li></ul><ul><li>-12x 7 y 10 </li></ul>
  • 41. Scientific Notation <ul><li>A number is expressed in scientific notation when it is written as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less then 10 </li></ul><ul><li>a x 10ⁿ, where 1 ≤ a < 10 </li></ul>
  • 42. Scientific Notation <ul><li>131,400,000,000= </li></ul><ul><li>1.314 x 10 11 </li></ul>Move the decimal behind the 1 st number How many places did you have to move the decimal? Put that number here!
  • 43. Write using scientific notation <ul><li>12,300= </li></ul><ul><li>1.23 x 10 4 </li></ul><ul><li>Write using standard notation </li></ul><ul><li>1.76 x 10 3 </li></ul><ul><li>1,760 </li></ul>
  • 44. Example – Scientific Notation <ul><li>131,400,000,000 = </li></ul><ul><li>5,284,000 </li></ul><ul><li>1.314 x 10 11 = </li></ul><ul><li>5.284 x 10 6 </li></ul>
  • 45. Example – Scientific Notation <ul><li>(5.2 x 10 9 )(3.0 x 10 -3 )= </li></ul><ul><li>(5.2 x 3.0) (10 9 x 10 -3 )= </li></ul><ul><li>15.6 x 10 6 </li></ul><ul><li>1.56 x 10 7 </li></ul><ul><li>2.45 x 10 -3 = </li></ul><ul><li>0.00245 </li></ul>
  • 46. Properties of Exponents a&b are real numbers, m&n are integers <ul><li>Product Property : a m * a n =a m+n </li></ul><ul><li>Quotient of Powers : a m = a m-n ; a≠0 a n </li></ul><ul><li>Power of a Power Property : (a m ) n =a mn </li></ul><ul><li>Power of a Product Property : (ab) m =a m b m </li></ul><ul><li>Negative Exponent Property : a -m = ; a ≠0 </li></ul><ul><li>Zero Exponent Property : a 0 =1; a≠0 </li></ul><ul><li>Power of Quotient: b≠0 </li></ul>

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