If `aDeltab = a^b + ab +a/b`, then `(9Delta3)` is equal to :

Options

A. 729
B. 927
C. 759
D. none of these

Answer

To solve the problem, we need to evaluate the expression \(9 \Delta 3\) using the given definition of the operation \(a \Delta b\).

### Step-by-Step Solution:

1. **Understand the operation**: We have the operation defined as:
\[ a \Delta b = a^b + ab + \frac{a}{b} \]

2. **Substitute the values**: We need to find \(9 \Delta 3\). Here, \(a = 9\) and \(b = 3\). So we substitute these values into the operation:
\[ 9 \Delta 3 = 9^3 + 9 \cdot 3 + \frac{9}{3} \]

3. **Calculate \(9^3\)**:
\[ 9^3 = 729 \]

4. **Calculate \(9 \cdot 3\)**:
\[ 9 \cdot 3 = 27 \]

5. **Calculate \(\frac{9}{3}\)**:
\[ \frac{9}{3} = 3 \]

6. **Add all the results together**: Now we sum the results from the previous calculations:
\[ 9 \Delta 3 = 729 + 27 + 3 \]

7. **Perform the addition**:
- First, add \(729 + 27\):
\[ 729 + 27 = 756 \]
- Then, add \(756 + 3\):
\[ 756 + 3 = 759 \]

8. **Final Result**: Therefore, the value of \(9 \Delta 3\) is:
\[ 9 \Delta 3 = 759 \]