To solve the expression $(3d^4)^2$, we need to apply the power rule for exponents, which states that $(a^m)^n = a^{m \cdot n}$.

Starting with $(3d^4)^2$:

1. Apply the exponent to both the constant and the variable inside the parentheses: $(3d^4)^2 = 3^2 \cdot (d^4)^2$

2. Simplify each part:

   • $3^2 = 9$
   • $(d^4)^2 = d^{4 \cdot 2} = d^8$

Thus, the simplified expression is: $9d^8$

The correct answer is B.

Would you like further details on any part of this? Here are five related questions to deepen your understanding:

1. How do you handle exponents when multiplying expressions with the same base?
2. What is the general rule for raising a product to a power?
3. How would you simplify $(2x^3)^4$?
4. Can you explain the difference between distributing powers over addition versus multiplication?
5. What is the result of raising a power to a power in expressions like $(y^5)^3$?

Tip: Always apply the exponent to every term inside the parentheses, including both constants and variables!