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The given problem asks: 

Which of the following is equivalent to \(\left( \frac{3}{5} \right)^{2x}\)?

### Step-by-Step Analysis:

The original expression is \(\left( \frac{3}{5} \right)^{2x}\), and we want to find an expression from the choices that is equivalent to this.

- Using properties of exponents, we can rewrite \(\left( \frac{3}{5} \right)^{2x}\) as:
  \[
  \left( \frac{3}{5} \right)^{2x} = \left( \left( \frac{3}{5} \right)^2 \right)^x = \left( \frac{3^2}{5^2} \right)^x = \left( \frac{9}{25} \right)^x
  \]

So, \(\left( \frac{3}{5} \right)^{2x}\) simplifies to \(\left( \frac{9}{25} \right)^x\).

### Answer:
The correct option is the last one: \(\left( \frac{9}{25} \right)^x\).

Would you like more details or have any further questions?

### Related Questions:
1. How can we apply exponent rules to fractions?
2. What is the process for expanding powers like \(\left( \frac{a}{b} \right)^n\)?
3. What are some common mistakes when working with exponent rules?
4. How does simplifying exponents help solve more complex algebraic expressions?
5. Can exponent rules be applied to negative fractions in the same way?

### Tip:
When simplifying expressions with powers of fractions, always apply the exponent to both the numerator and denominator.

Which of the following is equivalent to (3/5)^(2x)?

Learn how to simplify the exponential fraction (3/5)^(2x) using exponent rules. This problem involves applying the exponent to both the numerator and the denominator. Suitable for students in Grades 8-10.

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