Final answer:
The simplification of the expression 4d^3/8 yields d^3/2, which is not represented by any provided answer options. If converted to a radical and accounting for potential typos, it could be expressed as the cubed root of d^9, though this is still not an available option.
Step-by-step explanation:
The student's question concerns simplifying the expression 4d^3/8. To approach this, we recognize that the fraction can be simplified by dividing both numerator and denominator by the common factor of 4, resulting in d^3/2. However, none of the provided answer options are correct simplifications of the initial expression. If we were actually seeking a radical form of the expression, and assuming there might be a typo in the question, we could convert the simplified expression into a radical by saying that d^3/2 is equivalent to the cubed root of d raised to the 9th power, since 3 multiplied by 3 equals 9 (using the property of cubing of exponentials).
However, this is not one of the provided options, indicating either a mistake in the question's presented options or a misunderstanding of the original expression.