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Let's solve the problem step by step. Here's the given expression:

\[
\frac{\left(-\frac{4}{5}\right)^2}{\left(-\frac{1}{4} - \frac{1}{2} \times \frac{3}{4}\right)}
\]

### Step 1: Simplify the numerator
The numerator is \(\left(-\frac{4}{5}\right)^2\). Squaring a negative fraction makes it positive:

\[
\left(-\frac{4}{5}\right)^2 = \frac{16}{25}.
\]

### Step 2: Simplify the denominator
The denominator involves two terms: 
\[
-\frac{1}{4} - \frac{1}{2} \times \frac{3}{4}.
\]

#### Step 2.1: Simplify \(\frac{1}{2} \times \frac{3}{4}\)
Multiply the fractions:
\[
\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}.
\]

#### Step 2.2: Subtract from \(-\frac{1}{4}\)
Now compute:
\[
-\frac{1}{4} - \frac{3}{8}.
\]

To subtract, find a common denominator. The least common denominator of 4 and 8 is 8:
\[
-\frac{1}{4} = -\frac{2}{8}.
\]

Thus:
\[
-\frac{2}{8} - \frac{3}{8} = -\frac{5}{8}.
\]

The denominator is \(-\frac{5}{8}\).

### Step 3: Compute the division
Now divide the numerator by the denominator:
\[
\frac{\frac{16}{25}}{-\frac{5}{8}}.
\]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{16}{25} \div -\frac{5}{8} = \frac{16}{25} \times -\frac{8}{5}.
\]

Multiply the numerators and denominators:
\[
\frac{16}{25} \times -\frac{8}{5} = \frac{16 \cdot -8}{25 \cdot 5} = \frac{-128}{125}.
\]

### Final Answer:
\[
\boxed{-\frac{128}{125}}
\]

Would you like further clarifications or explanations? 

---

### Follow-Up Questions:
1. Can you simplify \(\frac{-128}{125}\) into a mixed number?  
2. How do you find the reciprocal of a fraction?  
3. What is the significance of squaring a fraction like \(\left(-\frac{4}{5}\right)^2\)?  
4. Can this problem be solved using a calculator, and if so, how do you input fractions?  
5. What happens if one term in the denominator is zero?  

### Tip:
Always simplify each component of a complex fraction separately before combining them—it reduces errors!

Evaluate the expression (-4/5)^2 ÷ (-1/4 - 1/2 × 3/4). Write your answer as a fraction or as a whole or mixed number.

Step-by-step solution to evaluate (-4/5)^2 ÷ (-1/4 - 1/2 × 3/4). Learn the concepts of fraction arithmetic, reciprocal rule, and squaring fractions. Suitable for Grades 6-8.

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