To solve \(\left( -2 \dfrac{3}{4} \right)^2\), follow these steps:

1. First, convert the mixed fraction into an improper fraction:
   \[
   -2 \dfrac{3}{4} = -\dfrac{8}{4} - \dfrac{3}{4} = -\dfrac{11}{4}
   \]

2. Now, square the improper fraction:
   \[
   \left( -\dfrac{11}{4} \right)^2 = \dfrac{(-11)^2}{4^2} = \dfrac{121}{16}
   \]

Thus, \(\left( -2 \dfrac{3}{4} \right)^2 = \dfrac{121}{16}\).

Would you like further details or clarifications?

Here are some related questions:
1. How do you simplify a mixed fraction?
2. What is the general rule for squaring negative numbers?
3. How do you convert a mixed fraction to an improper fraction?
4. How do you perform fraction multiplication?
5. How does squaring affect the sign of a negative number?

**Tip**: Always convert mixed fractions to improper fractions before performing arithmetic operations.

Learn how to square the mixed fraction (-2 3/4)^2 with a step-by-step solution. This guide covers converting mixed fractions to improper fractions and applying exponentiation rules. Suitable for students in Grades 6-8.

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