To simplify the expression $\left(\frac{5}{2}\right)^{-3}$, you can follow these steps:

1. Apply the negative exponent rule: The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$. So, $\left(\frac{5}{2}\right)^{-3} = \frac{1}{\left(\frac{5}{2}\right)^3}$

2. Raise the fraction to the positive power: Now, calculate $\left(\frac{5}{2}\right)^3$: $\left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8}$

3. Take the reciprocal: Since the exponent was negative, you take the reciprocal: $\frac{1}{\frac{125}{8}} = \frac{8}{125}$

So, $\left(\frac{5}{2}\right)^{-3} = \frac{8}{125}$.

Would you like more details or have any questions?

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Here are five related questions you might find interesting:

1. What is $\left(\frac{3}{4}\right)^{-2}$?
2. How do you simplify $\left(\frac{2}{3}\right)^{-4}$?
3. What is the result of $7^{-2}$?
4. How does the negative exponent rule apply to decimals, such as $0.5^{-2}$?
5. How would you simplify $\left(\frac{5}{3}\right)^{0}$?

Tip: Remember that a negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent!