Final answer:
To simplify the expression (2u³w²)³(-2u³)w³)², we raise each term to the appropriate power and then combine like terms.
Step-by-step explanation:
To simplify the expression (2u³w²)³(-2u³)w³)², we need to follow the order of operations and raise each term to the appropriate power. First, let's simplify the expression inside the first set of parentheses: (2u³w²)³ = 2³u³³w²³ = 8u⁹w⁶. Next, let's simplify the expression inside the second set of parentheses: (-2u³)w³ = (-2)³u³³w³ = -8u⁹w⁹. Finally, let's raise the entire expression to the power of 2: (8u⁹w⁶ -8u⁹w⁹)² = (64u¹⁸w¹² - 64u¹⁸w¹⁸).