## Fractional Exponent: proper answer for 2 ^5/2 - 2^3/2 ?

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### Fractional Exponent: proper answer for 2 ^5/2 - 2^3/2 ?

2 ^5/2 - 2^3/2, if i typped that write should be 2 to the 5/2 power minus 2 to the 3/2 power. I read the explanation on the site but I can not figure out how to get a proper answer. It was a sample question for an assessment, the listed is 2^3/2 power. But can not figure out how to get there. Please help!
neo_kalel

Posts: 1
Joined: Sat May 16, 2009 5:45 pm

neo_kalel wrote:2 ^5/2 - 2^3/2, if i typped that write should be 2 to the 5/2 power minus 2 to the 3/2 power.

To learn how to format math by just typing, try here.

In LaTeX form, I think you mean the expression to be as follows:

. . . . .$2^{\frac{5}{2}}\, -\, 2^{\frac{3}{2}}$

I suspect that the instructions are to "simplify" or to "express as a single radical term". If so, then you can learn the basics of radicals here and about fractional exponents here.

Once you've studied the above, then the below should seem sensible:

. . . . .$2^{\frac{5}{2}}\, =\, 2^{2\, +\, \frac{1}{2}}\, =\, (2^2)(2^{\frac{1}{2}}\, =\, 4\sqrt{2}$

. . . . .$2^{\frac{3}{2}}\, =\, 2^{1\, +\, \frac{1}{2}}\, =\, (2)(2^{\frac{1}{2}}\, =\,2\sqrt{2}$

...and so forth.

stapel_eliz

Posts: 1803
Joined: Mon Dec 08, 2008 4:22 pm