Question 24633
i assume you mean this: {{{((2x^(-4)y^3)/(xy^2))^(-2)}}}

First thing is to start combining terms, to get rid of the brackets, so you can see what you have. Do not concern yourself with "should it be positive"...just leave everything as it is and work with that...


So, first I will do the division...which means the powers subtract!
{{{((2x^(-4)y^3)/(xy^2))^(-2)}}}
{{{((2x^(-5)y^3)/(y^2))^(-2)}}}
{{{(2x^(-5)y)^(-2)}}}


Now we have 1 polynomial raised to the power -2. 
At this point I would do the following re-arrangement of the polynomial (it isn't necessary though...you can keep the x term with the others, but you are more likely to make mistakes):


{{{((2y)/(x^5))^(-2)}}}


Now i shall convert this to a +2 power. this is done by inverting the whole polynomial..that is the meaning of a -ve power.


So, we have {{{((x^5)/(2y))^2}}}
which is then {{{(x^10)/(4y^2)}}}


jon