Final answer:
The expression (4x³y³)(2x²y) simplifies to 8x⁵y⁴ by multiplying coefficients and adding exponents of like bases. The correct answer is option D) 8x⁵y⁴.
Step-by-step explanation:
To simplify the expression (4x³y³)(2x²y), we need to apply the rules for multiplying exponential terms. When two exponentiated terms with the same base are multiplied, we keep the base and add the exponents. We apply this to both the x terms and the y terms separately.
First, for the x terms: 4x³ × 2x² = 8x⁵, because 4 × 2 = 8 and x³ × x² = x⁵ (3 + 2 = 5).
Second, for the y terms: y³ × y = y⁴, because y⁵ is implied to have an exponent of 1, and y³ × y¹ = y⁴ (3 + 1 = 4).
Putting these together gives us the simplified expression: 8x⁵y⁴, which corresponds to option D) 8x⁵y⁴.