**Simplifying the Expression | cos x{sin x (sin^2x sin^2y)sqrt} |**

To simplify the given expression, we need to follow the order of operations (PEMDAS/BODMAS) and apply the trigonometric identities.

1. Evaluate the innermost parentheses:
- (sin^2x sin^2y)

This expression represents the product of the squares of the sine values of angles x and y. There are no additional simplifications we can make at this point.

2. Simplify the expression inside the curly braces:
- sin x (sin^2x sin^2y)

We can rewrite this as sin x * sin^2x * sin^2y.

3. Apply the trigonometric identity:
- sin^2θ = (1 - cos 2θ) / 2

We can use this identity to rewrite each sin^2 term in terms of cos 2θ.

4. Substituting the trigonometric identity:
- sin x * [(1 - cos 2x) / 2] * [(1 - cos 2y) / 2]

Now, we have expressed each sin^2 term in terms of cos.

5. Simplify the expression:
- sin x * (1 - cos 2x) * (1 - cos 2y) / 4

We can simplify the expression by multiplying everything together and dividing by 4.

6. Apply the trigonometric identity:
- cos 2θ = 2cos^2θ - 1

We can use this identity to rewrite each cos 2θ term.

7. Substituting the trigonometric identity:
- sin x * (1 - (2cos^2 2x - 1)) * (1 - (2cos^2 2y - 1)) / 4

Now, we have expressed each cos 2θ term in terms of cos.

8. Simplify the expression:
- sin x * (2 - 2cos^2 2x) * (2 - 2cos^2 2y) / 4

We can simplify the expression by expanding and simplifying each binomial term.

9. Apply the trigonometric identity:
- cos^2θ = (1 + cos 2θ) / 2

We can use this identity to rewrite each cos^2 term.

10. Substituting the trigonometric identity:
- sin x * (2 - 2((1 + cos 4x) / 2)) * (2 - 2((1 + cos 4y) / 2)) / 4

Now, we have expressed each cos^2 term in terms of cos.

11. Simplify the expression:
- sin x * (2 - (1 + cos 4x)) * (2 - (1 + cos 4y)) / 4

We can simplify the expression by expanding and simplifying.

12. Simplify further:
- sin x * (1 - cos 4x) * (1 - cos 4y) / 4

We can simplify the expression by multiplying everything together.

13. Simplify the outermost brackets:
- cos x * sin x * (1 -