To divide the expression (x⁸y⁸ + 2x⁵y⁵ + 7x³y³) by (-x²y²), we can use the rules of exponents and division.

First, let's simplify the expression (-x²y²) by multiplying it with -1:
(-x²y²) = -1 * x² * y² = -x²y²

Now, let's divide each term of the numerator by the denominator:

x⁸y⁸ / (-x²y²) = (x⁸ / x²) * (y⁸ / y²) = x⁶ * y⁶

2x⁵y⁵ / (-x²y²) = (2x⁵ / x²) * (y⁵ / y²) = 2x³ * y³

7x³y³ / (-x²y²) = (7x³ / x²) * (y³ / y²) = 7x * y

Therefore, the division of the expression (x⁸y⁸ + 2x⁵y⁵ + 7x³y³) by (-x²y²) is:

x⁶y⁶ + 2x³y³ + 7xy