How do you simplify #((3^-2 x^5 y^-5)^10 (3^3 x^-5 y^2)^3)/((3^5 x^-3 y^4)^2)#?
This problem isn't hard conceptually; it's just painstaking.
1) Clear the parentheses by raising all the powers inside the parentheses by the powers outside.
To raise a power to a power, you multiply.
2) Clear the negative exponents by flipping them to the opposite side of the fraction bar and reversing the negative signs to positive
3) Group like bases to make it easier to multiply them
4) Multiply like bases
To multiply exponents, you add
5) Reduce by cancelling
To divide exponents, you subtract