What should come in place of question mark (?) in the following questions ?
`(81)^2xx(9)^8xx(729)^2=(9)^?`

Options

A. 11
B. 13
C. 14
D. None of these

Answer

To solve the equation \( (81)^2 \times (9)^8 \times (729)^2 = (9)^{?} \), we need to express all terms on the left side in terms of the base \( 9 \).

### Step 1: Rewrite each term in terms of base 9
1. **Convert \( 81 \)**:
\[ 81 = 9^2 \]
Therefore,
\[ (81)^2 = (9^2)^2 = 9^{2 \times 2} = 9^4 \]

2. **The term \( (9)^8 \)** remains as it is:
\[ (9)^8 = 9^8 \]

3. **Convert \( 729 \)**:
\[ 729 = 9^3 \]
Therefore,
\[ (729)^2 = (9^3)^2 = 9^{3 \times 2} = 9^6 \]

### Step 2: Combine the terms
Now we can rewrite the left side of the equation:
\[ (81)^2 \times (9)^8 \times (729)^2 = 9^4 \times 9^8 \times 9^6 \]

### Step 3: Use the property of exponents
Using the property of exponents that states \( a^m \times a^n = a^{m+n} \), we can combine the powers:
\[ 9^4 \times 9^8 \times 9^6 = 9^{4 + 8 + 6} \]

### Step 4: Calculate the sum of the exponents
Now, we calculate:
\[ 4 + 8 + 6 = 18 \]
Thus, we have:
\[ 9^{4 + 8 + 6} = 9^{18} \]

### Step 5: Set the equation
Now we can equate this to the right side of the original equation:
\[ 9^{18} = 9^{?} \]

### Step 6: Solve for the question mark
Since the bases are the same, we can equate the exponents:
\[ ? = 18 \]

### Final Answer
The value that should come in place of the question mark is:
\[ \boxed{18} \]

---