If the number of elements in the power set of set A is 128 then find the number of elements in the set A .

Explanation

To solve the problem, we need to find the number of elements in set A given that the number of elements in its power set is 128.

### Step-by-Step Solution:

1. **Understand the relationship between a set and its power set**:
The number of elements in the power set of a set A with n elements is given by the formula:
\[ \text{Number of elements in power set} = 2^n \]

2. **Set up the equation**:
According to the problem, the number of elements in the power set of set A is 128. Therefore, we can write:
\[ 2^n = 128 \]

3. **Express 128 as a power of 2**:
We need to express 128 in terms of powers of 2. We know that:
\[ 128 = 2^7 \]

4. **Equate the exponents**:
Since we have \(2^n = 2^7\), we can equate the exponents:
\[ n = 7 \]

5. **Conclusion**:
Therefore, the number of elements in set A is:
\[ \text{Number of elements in set A} = 7 \]

### Final Answer:
The number of elements in set A is **7**.