anonymous
  • anonymous
2 raised to the power of 5/2 - 2 raised to the power of 3/2
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
When you raise a power to a power you multiply the exponents.
anonymous
  • anonymous
well my answers are either A. 2 1/2 B. 2 C. 2 3/2 D. 2 5/3 or E. 2^2
anonymous
  • anonymous
Well, what is (5/2-2)(3/2)

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anonymous
  • anonymous
3/4?
anonymous
  • anonymous
\[(2^{\frac{5}{2}-2})^{\frac{3}{2}}\] \[= 2^{\frac{3}{2}(\frac{5}{2}-2)}\] \[= 2^{\frac{3}{2}\frac{5}{2} - \frac{3}{2}\frac{2}{1}}\] \[= 2^{\frac{15}{4} - \frac{12}{4}}\] \[= 2^{\frac{3}{4}}\]
anonymous
  • anonymous
Wait. I think you have a different problem.
anonymous
  • anonymous
thats not one of the answers ,the question is 2 raised to 5 over 2 subtract 2 raised to 3 over 2?
anonymous
  • anonymous
Yeah, you should put parens on that.. Do you mean \[2^{\frac{5}{2}} - 2^{\frac{3}{2}}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
Very different problem ;p
anonymous
  • anonymous
You can factor a 1/2 from the exponents.
anonymous
  • anonymous
Actually no you cannot.
anonymous
  • anonymous
That's just \(\sqrt{32} - \sqrt{8}\)
anonymous
  • anonymous
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
anonymous
  • anonymous
\(\sqrt{32} = \sqrt{2^2*2^2*2} = 2*2\sqrt{2} = 4\sqrt{2}\)
anonymous
  • anonymous
the answer is 2 and 3/2 but i dont no how they got that
anonymous
  • anonymous
\(\sqrt{8} = \sqrt{2^2*2} = 2\sqrt{2}\) \[\implies \sqrt{32} - \sqrt{8} = 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}\] So the answer should be \(2^{\frac{3}{2}}\)
anonymous
  • anonymous
where are you getting the square roots from
anonymous
  • anonymous
\(2^{\frac{1}{2}} = \sqrt{2}\)
anonymous
  • anonymous
im so confused
anonymous
  • anonymous
Well think about it this way then.
anonymous
  • anonymous
Multiplying powers of the same base you add their exponents. \(2^{5/2} \) \(= 2^{4/2} \bullet 2^{1/2}\) \(=2^2 \bullet 2^{1/2}\) \(= 4(2^{1/2})\)
anonymous
  • anonymous
Same for \(2^{3/2} = 2(2^{1/2})\)
anonymous
  • anonymous
So \(4(2^{1/2}) - 2(2^{1/2}) = 2(2^{1/2})\)
anonymous
  • anonymous
\(= 2^1* 2^{1/2} = 2^{1+1/2} = 2^{3/2}\)
anonymous
  • anonymous
so i just add 5/2 + 3/2?
anonymous
  • anonymous
no. Watch this series on exponents.. http://www.khanacademy.org/video/exponent-properties-1?playlist=Developmental%20Math
anonymous
  • anonymous
haha i did but i dont get subtraction... with exponents
anonymous
  • anonymous
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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