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.