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anonymous

  • 5 years ago

2 raised to the power of 5/2 - 2 raised to the power of 3/2

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  1. anonymous
    • 5 years ago
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    When you raise a power to a power you multiply the exponents.

  2. anonymous
    • 5 years ago
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    well my answers are either A. 2 1/2 B. 2 C. 2 3/2 D. 2 5/3 or E. 2^2

  3. anonymous
    • 5 years ago
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    Well, what is (5/2-2)(3/2)

  4. anonymous
    • 5 years ago
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    3/4?

  5. anonymous
    • 5 years ago
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    \[(2^{\frac{5}{2}-2})^{\frac{3}{2}}\] \[= 2^{\frac{3}{2}(\frac{5}{2}-2)}\] \[= 2^{\frac{3}{2}\frac{5}{2} - \frac{3}{2}\frac{2}{1}}\] \[= 2^{\frac{15}{4} - \frac{12}{4}}\] \[= 2^{\frac{3}{4}}\]

  6. anonymous
    • 5 years ago
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    Wait. I think you have a different problem.

  7. anonymous
    • 5 years ago
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    thats not one of the answers ,the question is 2 raised to 5 over 2 subtract 2 raised to 3 over 2?

  8. anonymous
    • 5 years ago
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    Yeah, you should put parens on that.. Do you mean \[2^{\frac{5}{2}} - 2^{\frac{3}{2}}\]

  9. anonymous
    • 5 years ago
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    yes

  10. anonymous
    • 5 years ago
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    Very different problem ;p

  11. anonymous
    • 5 years ago
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    You can factor a 1/2 from the exponents.

  12. anonymous
    • 5 years ago
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    Actually no you cannot.

  13. anonymous
    • 5 years ago
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    That's just \(\sqrt{32} - \sqrt{8}\)

  14. anonymous
    • 5 years ago
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    if i do 2 5/2 divided by half i get 9 and if i do 2 3/2 divided by half i get 7 so if i subtract them i obviously get 2 which is b but i dont think thats right

  15. anonymous
    • 5 years ago
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    \(\sqrt{32} = \sqrt{2^2*2^2*2} = 2*2\sqrt{2} = 4\sqrt{2}\)

  16. anonymous
    • 5 years ago
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    the answer is 2 and 3/2 but i dont no how they got that

  17. anonymous
    • 5 years ago
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    \(\sqrt{8} = \sqrt{2^2*2} = 2\sqrt{2}\) \[\implies \sqrt{32} - \sqrt{8} = 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}\] So the answer should be \(2^{\frac{3}{2}}\)

  18. anonymous
    • 5 years ago
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    where are you getting the square roots from

  19. anonymous
    • 5 years ago
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    \(2^{\frac{1}{2}} = \sqrt{2}\)

  20. anonymous
    • 5 years ago
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    im so confused

  21. anonymous
    • 5 years ago
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    Well think about it this way then.

  22. anonymous
    • 5 years ago
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    Multiplying powers of the same base you add their exponents. \(2^{5/2} \) \(= 2^{4/2} \bullet 2^{1/2}\) \(=2^2 \bullet 2^{1/2}\) \(= 4(2^{1/2})\)

  23. anonymous
    • 5 years ago
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    Same for \(2^{3/2} = 2(2^{1/2})\)

  24. anonymous
    • 5 years ago
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    So \(4(2^{1/2}) - 2(2^{1/2}) = 2(2^{1/2})\)

  25. anonymous
    • 5 years ago
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    \(= 2^1* 2^{1/2} = 2^{1+1/2} = 2^{3/2}\)

  26. anonymous
    • 5 years ago
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    so i just add 5/2 + 3/2?

  27. anonymous
    • 5 years ago
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    no. Watch this series on exponents.. http://www.khanacademy.org/video/exponent-properties-1?playlist=Developmental%20Math

  28. anonymous
    • 5 years ago
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    haha i did but i dont get subtraction... with exponents

  29. anonymous
    • 5 years ago
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    That's because you can't do anything special when you are adding and subtracting exponents. You can only factor out common factors. But in this case you have a common factor of 2^{1/2} that you can pull out of each term.

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