which of the following interpretations for the given expression is correct

Answer: the first option, the cube of the of difference of 5 times the square of y and 7 divided by the square of 2 times y.

Justification:

Let's follow the word instructions step-by step

1) The cube of the difference means that you have to write the difference and then make the cube of that. So it were the difference of x and y, the cube of the difference is (x - y)^3.

2) But it is not the difference of x and y, it is the difference of 5 times the square of y and 7.

The difference of 5 times the square of y and 7 is 5y^2 - 7.

Its cube is (5y^2 - 7)^3

3) Now the expression resulted in the point 2 has to be divides by the square of 2 tmes y.

The square of 2 times y is (2y)^2.

Then, the division leads to the expression:

    (5y^2 - 7)^3
--------------------
      (2y)^2

Which is the given expression.