$$ \left(\frac{36}{175}^{}\right)^{-1} $$

To simplify the expression $\left(\frac{36}{175}\right)^{-1}$, you need to find the reciprocal of the fraction. Here's the step-by-step process:

1. **Understand the negative exponent rule**: 
   For any fraction $\frac{a}{b}$, $\left(\frac{a}{b}\right)^{-1} = \frac{b}{a}$.

2. **Apply the rule**:
   \[
   \left(\frac{36}{175}\right)^{-1} = \frac{175}{36}
   \]

So, the simplified form of $\left(\frac{36}{175}\right)^{-1}$ is:

\[
\frac{175}{36}
\]

Would you like more details or have any questions? Here are some related topics you might find interesting:

1. Understanding and simplifying expressions with negative exponents.
2. How to find the reciprocal of a fraction.
3. Simplifying complex expressions with exponents.
4. Using exponents in algebraic equations.
5. Practical applications of reciprocals in real-world problems.

**Tip:** A negative exponent indicates taking the reciprocal of the base. Always flip the fraction when you see $-1$ as the exponent!

Learn how to simplify the expression $\left(\frac{36}{175}\right)^{-1}$ using exponent rules. Understand the concept of negative exponents and how to find the reciprocal of a fraction step-by-step. Suitable for students in Grades 6-8.

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