1. **State the problem:** Simplify the expression $$(-6x^5 y^5)^4$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power: $$ (abc)^n = a^n b^n c^n $$ 3. **Apply the rule:** $$ (-6x^5 y^5)^4 = (-6)^4 (x^5)^4 (y^5)^4 $$ 4. **Calculate each part:** - $$(-6)^4 = (-6) \times (-6) \times (-6) \times (-6) = 1296$$ - $$ (x^5)^4 = x^{5 \times 4} = x^{20} $$ - $$ (y^5)^4 = y^{5 \times 4} = y^{20} $$ 5. **Combine all parts:** $$ 1296 x^{20} y^{20} $$ 6. **Final answer:** $$ \boxed{1296 x^{20} y^{20}} $$