Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

3/4?

Answer 5

\[(2^{\frac{5}{2}-2})^{\frac{3}{2}}\]
\[= 2^{\frac{3}{2}(\frac{5}{2}-2)}\]
\[= 2^{\frac{3}{2}\frac{5}{2} - \frac{3}{2}\frac{2}{1}}\]
\[= 2^{\frac{15}{4} - \frac{12}{4}}\]
\[= 2^{\frac{3}{4}}\]

Answer 6

Wait. I think you have a different problem.

Answer 7

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

Answer 8

Yeah, you should put parens on that..
Do you mean

\[2^{\frac{5}{2}} - 2^{\frac{3}{2}}\]

Answer 9

yes

Answer 10

Very different problem ;p

Answer 11

You can factor a 1/2 from the exponents.

Answer 12

Actually no you cannot.

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

\(\sqrt{8} = \sqrt{2^2*2} = 2\sqrt{2}\)
\[\implies \sqrt{32} - \sqrt{8} = 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}\]
So the answer should be \(2^{\frac{3}{2}}\)

Answer 18

where are you getting the square roots from

Answer 19

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

Answer 20

im so confused

Answer 21

Well think about it this way then.

Answer 22

Multiplying powers of the same base you add their exponents.

\(2^{5/2} \)
\(= 2^{4/2} \bullet 2^{1/2}\)
\(=2^2 \bullet 2^{1/2}\)
\(= 4(2^{1/2})\)

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

no.
Watch this series on exponents..

http://www.khanacademy.org/video/exponent-properties-1?playlist=Developmental%20Math

Answer 28

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

Answer 29

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.