Let's break this down step by step.

We have the expression:

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

### Step 1: Solve the first part \(\left(\frac{-2}{3}\right)^2\)
\[
\left(\frac{-2}{3}\right)^2 = \frac{(-2)^2}{3^2} = \frac{4}{9}
\]

### Step 2: Convert the mixed number \(2 \frac{1}{3}\) to an improper fraction
\[
2 \frac{1}{3} = \frac{7}{3}
\]

### Step 3: Multiply \(\frac{3}{4}\) by \(\frac{7}{3}\)
\[
\frac{3}{4} \times \frac{7}{3} = \frac{21}{12} = \frac{7}{4}
\]

### Step 4: Combine the results
Now we have the expression:
\[
\frac{4}{9} - \frac{7}{4}
\]

### Step 5: Find a common denominator
The least common denominator (LCD) between 9 and 4 is 36. We convert the fractions:

\[
\frac{4}{9} = \frac{16}{36}
\]
\[
\frac{7}{4} = \frac{63}{36}
\]

### Step 6: Perform the subtraction
\[
\frac{16}{36} - \frac{63}{36} = \frac{16 - 63}{36} = \frac{-47}{36}
\]

Thus, the final result is:
\[
\frac{-47}{36}
\]

Would you like more details or have any questions? 

Here are some related questions:
1. How do you convert between improper fractions and mixed numbers?
2. What are the steps for finding a common denominator?
3. How do negative exponents affect fractions?
4. How do you simplify complex fractions?
5. Why is multiplying fractions easier than adding them?

**Tip:** When subtracting fractions, always remember to find the least common denominator to ensure accuracy.

Learn how to solve the expression (-2/3)^2 - 3/4 × 2 1/3 with a detailed step-by-step solution. This problem involves exponentiation of fractions, conversion of mixed numbers, and subtraction of fractions with a common denominator. Suitable for students in Grades 6-8.

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