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.