https://r2.erweima.ai/mathbot/image/1726879570803jfddpurv.jpg

It seems there was an issue processing the image using the OCR tool for the Spanish language. However, I can still manually analyze the content from the image. Based on the mathematical notation present, let's break down the expression:

The expression seems to involve the following operations:

\[
\left(\frac{\frac{12}{1 \times 2} - \frac{2 \times 2}{5}}{\frac{22}{11} \times \frac{15}{1 \times 2}}\right)^2
\]

### Step-by-step resolution:

1. **Handle the numerators and denominators separately**:
   - First, simplify the fractions inside the large parentheses.
   
2. **Simplify the first term in the numerator**:
   \[
   \frac{12}{1 \times 2} = \frac{12}{2} = 6
   \]

3. **Simplify the second term in the numerator**:
   \[
   \frac{2 \times 2}{5} = \frac{4}{5}
   \]

4. **Find a common denominator** for the two fractions:
   \[
   6 - \frac{4}{5} = \frac{30}{5} - \frac{4}{5} = \frac{26}{5}
   \]

   So, the numerator becomes \( \frac{26}{5} \).

5. **Simplify the denominator**:
   \[
   \frac{22}{11} \times \frac{15}{1 \times 2} = 2 \times \frac{15}{2} = 15
   \]

6. **Form the final expression**:
   \[
   \frac{\frac{26}{5}}{15} = \frac{26}{5 \times 15} = \frac{26}{75}
   \]

7. **Square the entire expression**:
   \[
   \left(\frac{26}{75}\right)^2 = \frac{26^2}{75^2} = \frac{676}{5625}
   \]

### Final Simplified Expression:
\[
\frac{676}{5625}
\]

This is the simplified version of the given expression. Would you like a further breakdown of any specific part?

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Here are 5 questions to deepen your understanding:
1. How do you find the least common multiple (LCM) when dealing with fractions?
2. What is the process of simplifying complex fractions step by step?
3. How do you apply exponentiation to fractions?
4. Why do we square both the numerator and the denominator separately?
5. What is the importance of simplifying fractions in algebraic operations?

**Tip:** Always simplify fractions and expressions before attempting more complex operations, like squaring or taking higher powers.

Resuelve la siguiente operación usando m.c.m. y simplificando al máximo la expresión: (12 / (1 * 2) - (2 * 2) / 5)^2 / (22 / 11 * 15 / (1 * 2))

Learn how to simplify complex fractions and apply exponentiation to fractions with a step-by-step solution to the problem: (12 / (1 * 2) - (2 * 2) / 5)^2 / (22 / 11 * 15 / (1 * 2)). This problem covers essential mathematical concepts like fractions, simplification, and exponentiation. Suitable for students in Grades 9-10.

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