Question 176298
First of all, I have to assume this is what you mean:
{{{(sqrt(32)x^5y^2)/(sqrt(2)x^3y^3)}}}
First, let's deal with sqrt(32).  Note that since 32=16*2, we can write it as
{{{sqrt(32)=sqrt(16*2)=sqrt(16)sqrt(2)=4sqrt(2)}}}
So we have
{{{(4sqrt(2)x^5y^2)/(sqrt(2)x^3y^3)}}}
Now, the sqrt(2) will cancel out, leaving:
{{{(4x^5y^2)/(x^3y^3)}}}
Now, there is x^5 on top and x^3 on bottom.  You can look at this two ways: if you were to write them out, you'd have xxxxx/xxx.  Three of the x's would cancel, leaving two on top, or x^2.  The rule is, when you have division, you subtract the exponents.  So x^5/x^3=x^(5-3)=x^2.  Similarly, with the y's we are left with one on the bottom.  So simplified we have:
{{{(4x^2)/y}}}