(–0.8xy root 2) divided by (0.4xy).

First, let's simplify the expression:

(-0.8xy√2) / (0.4xy)

Since the numerator and denominator both contain the variables x and y, they can be canceled out.

So, we have:

-0.8√2 / 0.4

Now, let's simplify the division of the numbers:

-0.8√2 / 0.4 = -2√2 / 1

Finally, we simplify further to get our answer:

-2√2 / 1 = -2√2