The question asks for the simplified form of the expression $\left(\frac{(2y^2)}{4y}\right)^4$.

Let's simplify it step by step:

Step 1: Simplify the inner fraction $\frac{2y^2}{4y}$

We can break this down as: $\frac{2y^2}{4y} = \frac{2}{4} \cdot \frac{y^2}{y}$ $\frac{2}{4} = \frac{1}{2}$ $\frac{y^2}{y} = y^{2-1} = y$ So, the fraction simplifies to: $\frac{1}{2} \cdot y = \frac{y}{2}$

Step 2: Raise the simplified expression to the power of 4

Now we need to compute $\left(\frac{y}{2}\right)^4$: $\left(\frac{y}{2}\right)^4 = \frac{y^4}{2^4} = \frac{y^4}{16}$

Final answer:

The simplified form of the expression is $\frac{y^4}{16}$.

Therefore, the correct answer is C.

Would you like further details on this solution or have any questions?

Here are 5 related questions for further practice:

1. Simplify $\left(\frac{3x^3}{6x}\right)^2$.
2. What is the simplified form of $\left(\frac{4a^2}{8b}\right)^3$?
3. Expand $\left(\frac{x^2}{2y}\right)^5$.
4. Simplify $\frac{(5y^3)}{10y^2}$.
5. Simplify $\left(\frac{7a^4}{14a^2}\right)^2$.

Tip: When dealing with powers, always simplify the base first before applying the exponent!