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!

Learn how to simplify the expression (5/2)^(-3) using the negative exponent rule with a step-by-step solution. This problem involves understanding exponents, negative exponents, and reciprocals. Suitable for Grades 6-8.

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