To simplify the expression (-3x⁵y) * (-2x^2y^2), we can multiply the coefficients and add the exponents of the variables.

The coefficient is -3 * -2 = 6.

The variable x has an exponent of 5 in the first term and 2 in the second term, so we add the exponents to get x^7.

The variable y has an exponent of 1 in the first term and 2 in the second term, so we add the exponents to get y^3.

Therefore, the simplified expression is 6x^7y^3.