To simplify the expression \(2(x^6y^2)^5 \cdot 3(-x^3y^2)^5\), we can break it down step-by-step.
Distribute the powers: \[ (x^6y^2)^5 = x^{6 \cdot 5}y^{2 \cdot 5} = x^{30}y^{10} \] \[ (-x^3y^2)^5 = (-1)^5 (x^3)^5 (y^2)^5 = -x^{15}y^{10} \]
Substituting back into the expression: \[ 2(x^6y^2)^5 \cdot 3(-x^3y^2)^5 = 2(x^{30}y^{10}) \cdot 3(-x^{15}y^{10}) \]
Combine coefficients and variables: \[ = 2 \cdot 3 \cdot (-1) \cdot x^{30} \cdot x^{15} \cdot y^{10} \cdot y^{10} = -6 x^{30 + 15} y^{10 + 10} \]
Combine the exponents: \[ = -6 x^{45} y^{20} \]
Thus, the final simplified expression is: \[ \boxed{-6 x^{45} y^{20}} \]