Question 113363
I presume you want to solve for x.


{{{x^(3/2)=125}}}.  This is equivalent to {{{(sqrt(x))^3=125}}}.  In general, {{{x^(a/b)=(root(b,x))^a}}}


So the first thing to do is to take the cube root of both sides of the equation:


{{{root(3,x^(3/2))=root(3,125)}}} 
{{{sqrt(x)=5}}}  (because 5 X 5 X 5 = 125, and because {{{x^(1/2)=sqrt(x)}}})


Then you need to square both sides:


{{{(sqrt(x))^2=5^2}}}


{{{x=25}}}.  Done.


By the way, the steps I used don't have to be done in that order.  We could have squared 125 to get 15625 and then taken the cube root of 15625 to get 25.  I did it the way I did because the numbers stayed smaller so the arithmetic was easier.


Hope this helps,
John