https://file.aiquickdraw.com/mathbot/file/17273211864697acgoqqb.jpg

Let's analyze the mathematical expression in the image. 

The problem is asking to evaluate the following expression given that \( x = 8 \) and \( y = 25 \):

\[
\frac{\frac{2x^3 \sqrt{y}}{x^3 + y^2}}{\frac{2}{x^3 + y^2}}
\]

First, let's simplify the given expression. The overall structure of the expression can be simplified by noticing that the denominators in the numerator and denominator are identical, which allows for a simplification.

Let me calculate it step by step.

1. **Substitute the values of \(x = 8\) and \(y = 25\) into the expression.**
   \[
   \frac{2 \cdot 8^3 \cdot \sqrt{25}}{8^3 + 25^2}
   \quad \text{and} \quad
   \frac{2}{8^3 + 25^2}
   \]

2. **Simplify the powers and roots.**
   - \( 8^3 = 512 \)
   - \( 25^2 = 625 \)
   - \( \sqrt{25} = 5 \)

   Substituting these values into the expression:

   \[
   \frac{2 \cdot 512 \cdot 5}{512 + 625}
   \quad \text{and} \quad
   \frac{2}{512 + 625}
   \]

3. **Simplify the expressions.**
   - \( 2 \cdot 512 \cdot 5 = 5120 \)
   - \( 512 + 625 = 1137 \)

   Now, the simplified expressions become:

   \[
   \frac{5120}{1137}
   \quad \text{and} \quad
   \frac{2}{1137}
   \]

4. **Divide the two expressions:**

   \[
   \frac{\frac{5120}{1137}}{\frac{2}{1137}} = \frac{5120}{2} = 2560
   \]

Thus, the value of the given expression is \( 2560 \).

This result does not match any of the provided answer choices (a through e), so there may be a typo in the provided options or expression.

Would you like further clarifications or details?

Here are five related questions to help deepen understanding:
1. What is the process of simplifying complex fractions?
2. How do you evaluate square roots and powers in a large expression?
3. What happens when you divide two fractions with the same denominator?
4. How can you identify when to cancel out terms in an expression?
5. How does substituting values help in simplifying algebraic expressions?

**Tip:** When faced with a complex fraction, always check for common denominators that can be canceled out to simplify the problem easily.

Jika x = 8 dan y = 25, nilai dari \(\frac{\frac{2x^3 \sqrt{y}}{x^3 + y^2}}{\frac{2}{x^3 + y^2}}\) adalah ....

Learn how to simplify a complex fraction given x = 8 and y = 25, using algebraic principles involving exponents and radicals. This problem involves simplifying the expression \(\frac{\frac{2x^3 \sqrt{y}}{x^3 + y^2}}{\frac{2}{x^3 + y^2}}\) step-by-step, suitable for Grades 9-11.

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