Final answer:
The simplification of the expression (3d²×4d)³ results in 1728d¹, which is not among the provided choices. To simplify, we multiply the coefficients and sum the exponents, then apply the result to the power.
Step-by-step explanation:
The student is asking to simplify the expression (3d²×4d)³. First, we multiply 3d² and 4d together to get 12d³. Next, we raise this result to the third power. Remember, when we raise a product to a power, we raise both the coefficient (the number) and the variable to that power. To find the cube of 12 (12³), we calculate 12×12×12 which equals 1728. As for the variable with its exponent (d³), we apply the Cubing of Exponentials rule which tells us to multiply the exponent by 3, so we get d³×3 which equals d¹. Combining these, the final simplified form is 1728d¹.
The correct option is not listed in the student's choices, as the simplification results in 1728d¹, not d¶ as indicated in options a, b, c, and d.