Let be a binary operation on the set `Z^(+)`, given by `a^(**)b=2^(ab),a,binZ^(+)` then `1^(**)(2^(**)3)` is

Options

A. `2^(12)`
B. `2^(64)`
C. `2^(0)`
D. None of these

Answer

To solve the problem, we need to evaluate the expression \(1^{(**)}(2^{(**)}3)\) using the defined binary operation \(a^{(**)}b = 2^{(ab)}\).

### Step-by-step Solution:

1. **Evaluate \(2^{(**)}3\)**:
- Here, \(a = 2\) and \(b = 3\).
- According to the operation defined, we have:
\[ 2^{(**)}3 = 2^{(2 \cdot 3)} = 2^{6} \]
- Calculate \(2^6\):
\[ 2^6 = 64 \]

2. **Now evaluate \(1^{(**)}(2^{(**)}3)\)**:
- We found that \(2^{(**)}3 = 64\), so we now need to compute \(1^{(**)}64\).
- Here, \(a = 1\) and \(b = 64\).
- Using the operation defined:
\[ 1^{(**)}64 = 2^{(1 \cdot 64)} = 2^{64} \]

3. **Final Calculation**:
- The value of \(2^{64}\) is a large number, but we can leave it in exponential form for the answer.

### Final Answer:
\[ 1^{(**)}(2^{(**)}3) = 2^{64} \]