Question 31253
You can use the following rule to get rid of negative exponents:

{{{X^(-n) = 1/(X^n)}}}

or equivalently:
{{{1/X^(-n) = X^n}}}

So you can make the exponent positive, but you must also change the X value to its reciprocal. For example,

{{{3^(-2) = 1/3^2 = 1/9}}}
{{{1/3^(-2) = 3^2 = 9}}}

Let's apply this rule to your equation, and "convert" all the exponents to positive numbers:
{{{xy^2 - 3xy/y^(-1) + 2x^0y^2/x^(-1) - 4x^2/(y^2) + 2x^2y^(-2) = xy^2 - 3xy*y + 2*1*y^2*x - 4x^2/(y^2) + 2x^2/(y^2)}}}

This is the same as:
{{{xy^2 - 3xy^2 + 2x*y^2 - 4x^2/(y^2) + 2x^2/(y^2)}}}
The first 3 terms cancel out. So we're left just with:
{{{- 4x^2/(y^2) + 2x^2/(y^2) = -2x^2/(y^2)}}}
We can further reduce this by grouping x^2 and y^2:
{{{-2(x/y)^2}}}

And this is as far as we can go.


I hope this helps!
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