Rationalize the denominator and simplify the quad?root of 2x^5/3w

Question

anonymous · Answer

$$\sqrt[4]{2x ^{5}/3w}$$

anonymous · Answer

I came up with $$x ^{4}\sqrt{(54w ^{3}x)/3w}$$ but it looks wrong to me

anonymous · Answer

I'm confused >.<

anonymous · Answer

ok multiply and divide by 81w^4

anonymous · Answer

oh sorry...don't do that

anonymous · Answer

what you need is 81 w^4 inside the root

anonymous · Answer

so multiply divide  27w^3

anonymous · Answer

which you did right ?

anonymous · Answer

if you do that you will get 81w^4 in denominator which when comes out of the root becomes 3w

anonymous · Answer

Oh ok.. gotchya so far..

anonymous · Answer

in numerator you will get 54x^5 *w^3

anonymous · Answer

So multiply divide.. 27w^3 which yields to 81w^4 that becomes 3w out of the root to recap so far..

anonymous · Answer

yeah

anonymous · Answer

So I got the 54, where I messed up is the w and x

anonymous · Answer

i think it should become   x (54 * w^3* x)^1/4
                                    ---
                                      3w

anonymous · Answer

54 = 2*3*3*3 now you can't have anything else out of the root so the final should be 


x/3w  * ( 54*w^3*x)^1/4

anonymous · Answer

Ok.. thank you very much for you help with this.. these things are a pain in the butt to me >.<

anonymous · Answer

lolx.