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

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- anonymous

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

- katieb

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- anonymous

When you raise a power to a power you multiply the exponents.

- 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

Well, what is (5/2-2)(3/2)

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## More answers

- anonymous

3/4?

- 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

Wait. I think you have a different problem.

- anonymous

thats not one of the answers ,the question is 2 raised to 5 over 2 subtract 2 raised to 3 over 2?

- anonymous

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

- anonymous

yes

- anonymous

Very different problem ;p

- anonymous

You can factor a 1/2 from the exponents.

- anonymous

Actually no you cannot.

- anonymous

That's just \(\sqrt{32} - \sqrt{8}\)

- 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

\(\sqrt{32} = \sqrt{2^2*2^2*2} = 2*2\sqrt{2} = 4\sqrt{2}\)

- anonymous

the answer is 2 and 3/2 but i dont no how they got that

- 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

where are you getting the square roots from

- anonymous

\(2^{\frac{1}{2}} = \sqrt{2}\)

- anonymous

im so confused

- anonymous

Well think about it this way then.

- 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

Same for \(2^{3/2} = 2(2^{1/2})\)

- anonymous

So
\(4(2^{1/2}) - 2(2^{1/2}) = 2(2^{1/2})\)

- anonymous

\(= 2^1* 2^{1/2} = 2^{1+1/2} = 2^{3/2}\)

- anonymous

so i just add 5/2 + 3/2?

- anonymous

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

- anonymous

haha i did but i dont get subtraction... with exponents

- 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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