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anonymous

  • one year ago

check attachments please? thanks!

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    Problem 1. Do you know the definition of a rational (fraction) exponent?

  3. anonymous
    • one year ago
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    @mathstudent55 im afraid i don't

  4. mathstudent55
    • one year ago
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    \(\Huge a^{\frac{m}{n}} = \sqrt[n] {a^m} = (\sqrt[n]a)^m\)

  5. mathstudent55
    • one year ago
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    To find a rational power of a number, raise the number to the numerator of the exponent and take the root of the number the denominator tells you.

  6. mathstudent55
    • one year ago
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    Keep in mind: numerator -------> exponent denominator -----> root

  7. mathstudent55
    • one year ago
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    Examples: |dw:1438493658565:dw|

  8. mathstudent55
    • one year ago
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    |dw:1438493695962:dw|

  9. mathstudent55
    • one year ago
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    |dw:1438493741614:dw|

  10. mathstudent55
    • one year ago
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    Do you understand the examples?

  11. mathstudent55
    • one year ago
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    All the examples show you the same idea. The denominator of the exponent tells you which root to take. When the denominator is 2, you take the square root. When the denominator is 3 you take the cubic root, etc.

  12. mathstudent55
    • one year ago
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    The numerator tells you what power to raise the number to before or after you take the root.

  13. anonymous
    • one year ago
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    yes. i do. what i don't get is that when you get the result you get a single number, but my answer choices have the square root symbol would what you showed me still apply?

  14. mathstudent55
    • one year ago
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    Let's look at problem 1 now together.

  15. mathstudent55
    • one year ago
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    |dw:1438494095419:dw|

  16. mathstudent55
    • one year ago
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    What does the 2 in the denominator mean?

  17. anonymous
    • one year ago
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    numerator?

  18. mathstudent55
    • one year ago
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    From above: "The denominator of the exponent tells you which root to take."

  19. mathstudent55
    • one year ago
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    "When the denominator is 2, you take the square root. "

  20. mathstudent55
    • one year ago
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    A denominator of 2 means take the square root. |dw:1438494212377:dw|

  21. mathstudent55
    • one year ago
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    The numerator of 3 means raise the number to the 3rd power.

  22. mathstudent55
    • one year ago
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    What is \(2^3\) equal to?

  23. anonymous
    • one year ago
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    8. but what do you do with the denominator in the fraction?

  24. mathstudent55
    • one year ago
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    |dw:1438494329059:dw|

  25. mathstudent55
    • one year ago
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    The denominator of the exponent changed the problem from an exponent problem to a root problem.

  26. mathstudent55
    • one year ago
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    |dw:1438494376526:dw|

  27. anonymous
    • one year ago
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    OOHHHHHHHHHH OMG IM SO STUPIDDDD LOL

  28. mathstudent55
    • one year ago
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    No, you're not stupid. You're learning. I went through the same process you are going through now.

  29. mathstudent55
    • one year ago
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    Are you ready for problem 2?

  30. anonymous
    • one year ago
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    yup

  31. mathstudent55
    • one year ago
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    Here you will need a property of exponents. Here it is: \(\Huge \dfrac{a^m}{a^n} = a^{m - n} \) When you divide powers with the same base, write the same base and subtract the exponents.

  32. mathstudent55
    • one year ago
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    Here is an example of this rule: |dw:1438494620860:dw| Do you underrstand the example?

  33. anonymous
    • one year ago
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    yes

  34. mathstudent55
    • one year ago
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    OK. Now lets do problem 2.

  35. mathstudent55
    • one year ago
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    The first step is to use the rational exponents in reverse. Earlier, I explained how to handle a fraction as an exponent. In this problem, you are given a root in the numerator and a root in the denominator. We need to use the rule of rational exponents in reverse, and write the numerator and denominator of this fraction with fractions for the exponents.

  36. mathstudent55
    • one year ago
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    Let's just look at the numerator of our problem.

  37. mathstudent55
    • one year ago
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    |dw:1438494930324:dw|

  38. mathstudent55
    • one year ago
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    |dw:1438495081620:dw| We need to replace the box with an exponent. You need to work backwards, and figure out what fraction you need to raise 7 to to get the cubic root of 7. Remember above we saw that the denominator of an exponent tells you which root to take. Here we see we are taking the 3rd root (called the cubic root) of 7. If we take the cubic root of 7, what do we need in the denominator of the exponent?

  39. anonymous
    • one year ago
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    3?

  40. mathstudent55
    • one year ago
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    |dw:1438495150225:dw|

  41. mathstudent55
    • one year ago
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    Exaclty. Also, since we have just 7, not 7 raised to some power, that means the numerator is 1.

  42. mathstudent55
    • one year ago
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    |dw:1438495224736:dw|

  43. mathstudent55
    • one year ago
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    |dw:1438495237856:dw| Ok?

  44. anonymous
    • one year ago
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    alright

  45. mathstudent55
    • one year ago
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    Now let's look at the denominator. The denominator is similar to the numerator except instead of the cubic root, it's the fifth root.

  46. mathstudent55
    • one year ago
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    |dw:1438495324943:dw| What fraction is the exponent of 7?

  47. mathstudent55
    • one year ago
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    |dw:1438495375343:dw|

  48. anonymous
    • one year ago
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    |dw:1438495456106:dw| would this be it?

  49. mathstudent55
    • one year ago
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    Correct. Now let's put it together the way the problem is given. |dw:1438495483142:dw|

  50. mathstudent55
    • one year ago
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    Now you need the rule I gave you above. What do you do when you dived powers with the same base? You subtract the exponents. |dw:1438495589942:dw| What goes in the box?

  51. anonymous
    • one year ago
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    2/15 ?

  52. mathstudent55
    • one year ago
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    |dw:1438495725285:dw|

  53. mathstudent55
    • one year ago
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    Correct.

  54. anonymous
    • one year ago
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    thank you! can you help me with 1 last question?

  55. mathstudent55
    • one year ago
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    You're welcome. Sure, one more.

  56. anonymous
    • one year ago
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  57. mathstudent55
    • one year ago
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    Have you learned how to solve systems of equations by the addition method?

  58. anonymous
    • one year ago
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    im afraid not

  59. anonymous
    • one year ago
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    wouldn't the value of y be 8?

  60. mathstudent55
    • one year ago
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    We need to solve the system.

  61. anonymous
    • one year ago
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    wait i got this question. i sent the wrong picture wow

  62. mathstudent55
    • one year ago
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    Have you learned how to solve a system of equations by the substitution method?

  63. anonymous
    • one year ago
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    this was the one

  64. anonymous
    • one year ago
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    @mathstudent55 well turns out i did because in the snapshot there was no answer. but then i check on my page and it had the answer on it, so i probably figured out this morning

  65. mathstudent55
    • one year ago
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    Ok. I see.

  66. mathstudent55
    • one year ago
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    The graph of \(y = \sqrt x\) looks like this: |dw:1438496300889:dw|

  67. mathstudent55
    • one year ago
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    When you replace x by x - k, where k is a number, the graph shifts horizontally (left or right) k units.

  68. mathstudent55
    • one year ago
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    |dw:1438496428565:dw|

  69. mathstudent55
    • one year ago
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    If you compare \(y = \sqrt x\) with \(y = \sqrt{x + 7} \), you see that x was replaced by x + 7. That means that when you compare x + 7 with x - k, you see that it equals x - (-7). k = -7. Since k is a negative number, it means the graph shifts to the left. The 7 tells you it is a shift of 7 units left.

  70. mathstudent55
    • one year ago
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    |dw:1438496631995:dw|

  71. anonymous
    • one year ago
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    b and d are giving me some strong feelings for some reason. both of them feel right

  72. mathstudent55
    • one year ago
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    From the graphs of the choices, you see that: B is shifted 6 units left D is shifted 7 units left.

  73. anonymous
    • one year ago
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    d?

  74. anonymous
    • one year ago
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    @arindameducationusc do you know what the answer would be??

  75. arindameducationusc
    • one year ago
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    For question 1, 3 is for square power and 2 is for square root power... so apply that

  76. anonymous
    • one year ago
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    @arindameducationusc im afraid i have already answered question 1. I'm sorry for not informing you . i need 2

  77. arindameducationusc
    • one year ago
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    Just follow mathstudent steps... He is right

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