To Solve Problem 1.
We are going to begin by seperating the fraction into two parts (both still underneath one big -1st power)
This leads us to x^-3/y^2 + y^-3/x. After moving the powers to their correct locations we get:
1/(y^2*x^3) + 1(x*y^3).
Now factoring out 1/(x*y^2) from both sides we get.
1/(x*y^2)*[1/(x^2) + 1/(y)]
finding an LCD (least common denominator) for both fractions we can rewrite it as.
(1/x*y^2)*[(y + x^2)/(x^2*y)]
Placing back the factored fraction we end up with:
(y + x^2)/(x^3 * y^3)
and now applying the negative first power (REMEMBER FROM THE START!)
(x^3*y^3)/(y + x^2)
Is the correct answer.
To Solve Number 2.
We begin with the expression (3/(A^(-3) * B^(-2)))^(-2).
First we bring up the A and B (since we can w/ negative exponents!)
so we get (3*A^3 * B^2)^(-2). Now we can evaluate that -2nd power in two steps. First we evaluate it as a 2nd power and then a -1, both we know how to do.
So after evaluating the 2 we end up with:
After the -1 we end up with:
Which is what you should get! Good Luck :)