First thing is first. A negative power is just the reciprocal of the positive power. The reciprocal is just like flipping a fraction up-side down. Example; x^-2 = 1/x^2.
Next, when you multiply variables with different powers, you keep the variable and add the powers together. Ex; (x^3)(x^2) = x^5.
Last, when you divide variables with different powers, you subtract the power that is in the denominator from the power that is in the numerator. Ex; x^5 / x^2 = x^3.
If you understand all of that, then you should have no problem following this;
Each successive line will further simplify the equation.
y(x^-3/y^-5)^-1 × x(y^3/x^-3)^-3
y[(1/x^3) / (1/y^5)]^-1 × x[y^3 / (1/x^3)]^-3
y(y^5 / x^3)^-1 × x(y^3 x^3)^-3
y(x^3 / y^5) × x(1 / (y^3 x^3)^3)
yx^3 / y^5 × x(1 / (y^9 x^9))
x^3 / y^4 × x / (y^9 x^9)
x^3 / y^4 × 1 / (y^9 x^8)
x^3 / (y^13 x^8)
1 / (y^13 x^5)
That's your answer. And that is exactly what you posted above. Correct!