To solve \(\left( -\frac{3}{5} \right)^{-4}\), we use the following rules of exponents:

1. A negative exponent means we take the reciprocal of the base and make the exponent positive:
   \[
   \left( -\frac{3}{5} \right)^{-4} = \left( \frac{5}{-3} \right)^4
   \]

2. Now, raise both the numerator and the denominator to the power of 4:
   \[
   \left( \frac{5}{-3} \right)^4 = \frac{5^4}{(-3)^4}
   \]

3. Calculate the powers:
   \[
   5^4 = 625 \quad \text{and} \quad (-3)^4 = 81
   \]

4. Therefore:
   \[
   \left( -\frac{3}{5} \right)^{-4} = \frac{625}{81}
   \]

So, \(\left( -\frac{3}{5} \right)^{-4} = \frac{625}{81}\).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens when the exponent is positive for fractions with negative bases?
2. How do you simplify \(\left( \frac{2}{7} \right)^{-3}\)?
3. Can you explain why any number raised to the 0th power equals 1?
4. What is the result of \(\left( -\frac{4}{9} \right)^3\)?
5. How does changing the sign of the exponent affect the result?

**Tip:** When raising a fraction to a negative exponent, always take the reciprocal before applying the power.

Learn how to solve the expression (-3/5)^-4 step-by-step. This guide covers exponentiation with negative exponents, reciprocal operations, and raising fractions to a power. The final answer simplifies to 625/81. Suitable for students in Grades 8-10.

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