If `16xx8^(n+2)=2^(m)`, then m is equal to

Options

A. n + 8
B. 2n + 10
C. 3n + 2
D. 3n + 10

Answer

To solve the equation \( 16 \times 8^{(n+2)} = 2^m \), we will express all terms in the equation as powers of 2.

### Step-by-Step Solution:

1. **Rewrite 16 and 8 as powers of 2:**
\[ 16 = 2^4 \quad \text{and} \quad 8 = 2^3 \]
Therefore, we can rewrite the left side of the equation:
\[ 16 \times 8^{(n+2)} = 2^4 \times (2^3)^{(n+2)} \]

2. **Simplify \( 8^{(n+2)} \):**
Using the power of a power property \((a^m)^n = a^{m \cdot n}\):
\[ (2^3)^{(n+2)} = 2^{3(n+2)} = 2^{3n + 6} \]

3. **Combine the powers of 2:**
Now substitute back into the equation:
\[ 2^4 \times 2^{3n + 6} \]
Using the property \( a^m \times a^n = a^{m+n} \):
\[ 2^{4 + (3n + 6)} = 2^{3n + 10} \]

4. **Set the exponents equal:**
Since the bases are the same, we can equate the exponents:
\[ m = 3n + 10 \]

### Conclusion:
Thus, the value of \( m \) is:
\[ \boxed{3n + 10} \]