SAT problem

On the SAT Skills practice, it says I need to know how to "apply the properties of non-integer exponents."
It gives me this problem:

If x>0, which of the following are equivalent to (in here, there's a small x next to the denominator in the fraction 3/2)?

I. x sqr rt x
2. square root of x^3
3. (x^2) / square root of x

It says all three are correct.



Can anyone explain to me what all of this means? I'm totally lost...

self-bump

OK doke, you were given x raised to the power of the fraction 3/2.  The 3 is a familiar exponent like you know about first, while the 2, being the denominator, indicates a root, specifically square root.  So number 2 in the list of answers is most obviously correct.  Number 3 is seen correct if you apply the shortcut of subtracting exponents of same-base powers that are being divided.  2 minus 1/2 (square root is equivalent to exponent 1/2) equals 1 and 1/2 which equals 3/2.  Number 1 is seen correct if you apply the shortcut of adding exponents of same-base powers that are being multiplied.  You have x times square root x, so do 1 plus 1/2 equals 3/2.  (Remember that x has exponent 1, i.e. x = x^1.)

Oh... thanks, I didn't realize it was x raised to the 3/2. Thank you so much, I am soooo grateful.

>>4
:3