If `x =12 and y = 4, ` then the value of `(x + y) ^((x)/(y)) `is

Options

A. 48
B. 1792
C. 4096
D. 570

Answer

To solve the problem, we need to evaluate the expression \((x + y)^{(x/y)}\) given \(x = 12\) and \(y = 4\).

### Step-by-step Solution:

1. **Substitute the values of \(x\) and \(y\)**:
\[ x = 12, \quad y = 4 \]

2. **Calculate \(x + y\)**:
\[ x + y = 12 + 4 = 16 \]

3. **Calculate \(x/y\)**:
\[ \frac{x}{y} = \frac{12}{4} = 3 \]

4. **Substitute back into the expression**:
\[ (x + y)^{(x/y)} = 16^3 \]

5. **Calculate \(16^3\)**:
\[ 16^3 = 16 \times 16 \times 16 \]
First, calculate \(16 \times 16\):
\[ 16 \times 16 = 256 \]
Now, multiply \(256\) by \(16\):
\[ 256 \times 16 = 4096 \]

6. **Final Result**:
\[ (x + y)^{(x/y)} = 4096 \]

### Conclusion:
The value of \((x + y)^{(x/y)}\) is \(4096\).