Let's evaluate \(\left( -\frac{3}{2} \right)^2\).

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

When we multiply two negative numbers, the result is positive:

\[
\left( -\frac{3}{2} \right) \times \left( -\frac{3}{2} \right) = \frac{9}{4}
\]

Thus, \(\left( -\frac{3}{2} \right)^2 = \frac{9}{4}\).

Would you like further clarification, or do you have any other questions?

Here are some related questions:
1. What happens if we raise a negative fraction to an odd power?
2. How do we simplify higher powers of fractions, like \(\left(\frac{3}{2}\right)^4\)?
3. How can you apply the result of squaring a fraction in real-world scenarios?
4. What is the difference between squaring a negative number and cubing it?
5. How do you find the square root of \(\frac{9}{4}\)?

**Tip:** Remember that squaring a negative number always results in a positive value!

Explore how to square the negative fraction (-3/2) and learn how multiplying negative numbers results in a positive value. This problem demonstrates the application of exponentiation and fraction multiplication. Suitable for students in Grades 6-8.

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