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 given by the expression \( a \Delta b = a^b + ab + \frac{a}{b} \) for \( 9 \Delta 3 \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the values of \( a \) and \( b \)**:
- From the expression \( 9 \Delta 3 \), we identify \( a = 9 \) and \( b = 3 \).

2. **Substitute \( a \) and \( b \) into the expression**:
- We substitute \( a \) and \( b \) into the expression:
\[ 9 \Delta 3 = 9^3 + 9 \cdot 3 + \frac{9}{3} \]

3. **Calculate each term**:
- Calculate \( 9^3 \):
\[ 9^3 = 9 \times 9 \times 9 = 729 \]
- Calculate \( 9 \cdot 3 \):
\[ 9 \cdot 3 = 27 \]
- Calculate \( \frac{9}{3} \):
\[ \frac{9}{3} = 3 \]

4. **Add the results together**:
- Now, we add all the calculated values:
\[ 9 \Delta 3 = 729 + 27 + 3 \]
- Performing the addition:
\[ 729 + 27 = 756 \]
\[ 756 + 3 = 759 \]

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

### Final Answer:
\[ 9 \Delta 3 = 759 \]

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