What will come in the place of question mark in following questions.
`(?)^((4 xx 16 div 32 + 1)) + 12^(2) = 360`

Options

A. 4
B. 6
C. 8
D. 2

Answer

To solve the equation \( (?)^{(4 \times 16 \div 32 + 1)} + 12^2 = 360 \), we will follow these steps:

### Step 1: Rewrite the Equation
Let \( x = ? \). The equation can be rewritten as:
\[ x^{(4 \times 16 \div 32 + 1)} + 12^2 = 360 \]

### Step 2: Calculate \( 12^2 \)
First, calculate \( 12^2 \):
\[ 12^2 = 144 \]
Now, substitute this back into the equation:
\[ x^{(4 \times 16 \div 32 + 1)} + 144 = 360 \]

### Step 3: Isolate the Exponential Term
Next, isolate the term with \( x \):
\[ x^{(4 \times 16 \div 32 + 1)} = 360 - 144 \]
\[ x^{(4 \times 16 \div 32 + 1)} = 216 \]

### Step 4: Simplify the Exponent
Now, simplify the exponent \( 4 \times 16 \div 32 + 1 \):
1. Calculate \( 16 \div 32 \):
\[ 16 \div 32 = 0.5 \]
2. Now multiply by 4:
\[ 4 \times 0.5 = 2 \]
3. Finally, add 1:
\[ 2 + 1 = 3 \]
So, the exponent simplifies to 3. Now we have:
\[ x^3 = 216 \]

### Step 5: Solve for \( x \)
To find \( x \), take the cube root of both sides:
\[ x = \sqrt[3]{216} \]
Since \( 6^3 = 216 \), we find:
\[ x = 6 \]

### Final Answer
Thus, the value that comes in place of the question mark is:
\[ \boxed{6} \]