How do you simplify the expression (3x^2y)(4xy^3)?

To simplify the expression (3x^2y)(4xy^3), you multiply the numerical coefficients and then combine like terms (the variables).

First, look at the coefficients: you multiply 3 and 4, which gives you 12.

Next, for the variable parts, you handle each variable separately. For the x terms, you have x^2 from the first term and x from the second term. When multiplying with the same base, you add the exponents: 2 + 1 = 3, resulting in x^3.

For the y terms, you have y from the first term and y^3 from the second term. Again, you add the exponents: 1 + 3 = 4, giving you y^4.

Combining these results, you get 12 for the coefficient, x^3 for the x variable, and y^4 for the y variable. Therefore, the simplified expression is 12x^3y^4, which corresponds to the correct answer.