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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**.

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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!

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Learn how to simplify the algebraic expression \(\left(\frac{2y^2}{4y}\right)^4\) by applying exponent and fraction rules. This step-by-step solution covers key algebraic concepts such as exponents and simplifying rational expressions, suitable for students in Grades 8-10.

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