https://file.aiquickdraw.com/mathbot/file/1729303843859uc27rz4m.jpg

Let's work through the expressions you provided. There are two expressions to evaluate:

1. \(\left(\frac{3}{2}\right)^2 \div -2\)
2. \(-\left(\frac{5}{3}\right)^3\)

### First Expression: \(\left(\frac{3}{2}\right)^2 \div -2\)
1. First, square \(\frac{3}{2}\): 
   \[
   \left(\frac{3}{2}\right)^2 = \frac{9}{4}
   \]
2. Now divide by \(-2\), which is equivalent to multiplying by \(-\frac{1}{2}\):
   \[
   \frac{9}{4} \times -\frac{1}{2} = -\frac{9}{8}
   \]

So, the value of the first expression is \(-\frac{9}{8}\).

### Second Expression: \(-\left(\frac{5}{3}\right)^3\)
1. Cube \(\frac{5}{3}\):
   \[
   \left(\frac{5}{3}\right)^3 = \frac{125}{27}
   \]
2. Now apply the negative sign:
   \[
   -\frac{125}{27}
   \]

So, the value of the second expression is \(-\frac{125}{27}\).

### Final Answers:
1. First expression: \(-\frac{9}{8}\)
2. Second expression: \(-\frac{125}{27}\)

Let me know if you want any more details or have any questions!

Here are 5 related questions:
1. How do you multiply fractions and simplify the result?
2. What is the process for dividing fractions?
3. How does squaring a fraction affect its value?
4. What is the rule for applying a negative sign to an exponent result?
5. How would the results change if you squared a negative fraction?

**Tip:** When dividing by a fraction, you can multiply by its reciprocal instead, which can simplify the calculations.

Evaluate the following expressions as fractions:
1. (3/2)^2 ÷ -2
2. -(5/3)^3

Learn how to evaluate expressions with exponents and fractions, such as (3/2)^2 ÷ -2 and -(5/3)^3. This problem covers key concepts including exponentiation, division of fractions, and handling negative numbers. Suitable for students in Grades 8-10.

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