If the operation is defined by `a^(**)b=a+b-ab,` then `5^(**)` 7 equls

Options

A. 12
B. `-47`
C. `-23`
D. 35

Answer

To solve the problem using the defined operation \( a^{(**)}b = a + b - ab \), we will substitute \( a = 5 \) and \( b = 7 \) into the operation.

### Step-by-Step Solution:

1. **Identify the operation**: We know that \( a^{(**)}b = a + b - ab \).

2. **Substitute the values**: We need to find \( 5^{(**)}7 \). So we substitute \( a = 5 \) and \( b = 7 \):
\[ 5^{(**)}7 = 5 + 7 - 5 \cdot 7 \]

3. **Calculate \( 5 + 7 \)**:
\[ 5 + 7 = 12 \]

4. **Calculate \( 5 \cdot 7 \)**:
\[ 5 \cdot 7 = 35 \]

5. **Combine the results**: Now we substitute these results back into the equation:
\[ 5^{(**)}7 = 12 - 35 \]

6. **Perform the subtraction**:
\[ 12 - 35 = -23 \]

Thus, the final result is:
\[ 5^{(**)}7 = -23 \]