Final answer:
To simplify (3x²y) × (-2xy)³, cube the coefficient -2 to get -8, multiply the exponents of x and y, resulting in the simplified expression -8x⁵y⁴.
Step-by-step explanation:
To simplify the expression (3x²y) × (-2xy)³, we need to apply the rules of cubing of exponentials and multiplication of exponential terms.
Let's break it down step-by-step:
- Cube the coefficient of the second term, (-2) to the power of 3, which equals -8.
- Multiply the exponents of the x terms, remembering that when we multiply variables with the same base, we add their exponents, x² * (x³) thus becomes x^(2+3) or xµ.
- Repeat the same process with the y terms, y * (y³) becomes y^(1+3) or y⁴.
- Combine the results to get the simplified expression.
Therefore, the simplified expression is -8x⁵y⁴.