The expression you provided is:

\[
\left( -3 \dfrac{1}{3} \right)^2
\]

First, simplify the mixed number:

\[
-3 \dfrac{1}{3} = -\left( 3 + \dfrac{1}{3} \right) = -\dfrac{10}{3}
\]

Now, square the result:

\[
\left( -\dfrac{10}{3} \right)^2 = \dfrac{(-10)^2}{3^2} = \dfrac{100}{9}
\]

Thus, the value of the expression is:

\[
\boxed{\dfrac{100}{9}}
\]

Would you like more details or have any questions?

Here are 5 questions to deepen your understanding:
1. How do you convert mixed numbers to improper fractions?
2. Why does squaring a negative number result in a positive number?
3. How would you simplify the fraction \(\dfrac{100}{9}\) further?
4. What would the result be if the exponent was 3 instead of 2?
5. How does squaring fractions compare to squaring whole numbers?

**Tip:** Always simplify any mixed numbers before applying operations like squaring.

Learn how to square a mixed number, (-3 1/3)^2, by converting it into an improper fraction and applying exponent rules. This problem covers key concepts like mixed numbers, improper fractions, and squaring. Suitable for students in Grades 6-8.

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