Fill in the blanks
In the expression `((2)/(5))^(11)" "`, base =....., index = .....

Answer

To solve the question, we need to identify the base and the index in the expression \(\left(\frac{2}{5}\right)^{11}\).

### Step-by-step Solution:

1. **Understanding the Expression**: The expression \(\left(\frac{2}{5}\right)^{11}\) is in exponential form. This means that the fraction \(\frac{2}{5}\) is being multiplied by itself a certain number of times.

2. **Identifying the Base**: The base is the number that is being multiplied. In this case, the base is \(\frac{2}{5}\).

3. **Identifying the Index**: The index (also known as the exponent) tells us how many times the base is multiplied by itself. In this expression, the index is \(11\).

4. **Filling in the Blanks**:
- Base = \(\frac{2}{5}\)
- Index = \(11\)

### Final Answer:
- Base = \(\frac{2}{5}\)
- Index = \(11\)