do the indicated operations and write with only positive exponents and assume all variables are nonzero real numbers

x^-5 y^7/x^-2 y^5

y^2/x^3

x^3=0

your x^-5 y^7/x^-2 y^5 should have said

x^-5 y^7/(x^-2 y^5) then it would be

y^2/x^3 as you had,

but I don't see what the x^3=0 in your last line is supposed to be.
Is it supposed to say x^3 is not equal to zero??
then it should be placed after you second last line as a restriction.

I meant to put y^2/x^3 as my answer. Is that correct?

To simplify the expression and write it with only positive exponents, you can use the rules of exponents.

For the first expression: (x^-5 y^7) / (x^-2 y^5)

Step 1: Apply the division rule of exponents. Subtract the exponents of x and y:
x^(-5-(-2)) y^(7-5)

Step 2: Simplify the powers of x and y:
x^(-5+2) y^2

Step 3: Negative exponents represent reciprocals. Hence, rewrite x^(-5+2) as 1/x^3:
1/x^3 y^2

The first expression simplified to 1/x^3 y^2.

For the second expression: (y^2) / (x^3)

This expression is already in a form with positive exponents. No further simplification is needed.

Regarding the equation x^3 = 0, it means that x raised to the power of 3 equals zero. However, there is no real number that can be raised to any power and result in zero. So, there is no real solution for this equation.