If `sqrt(2^(n))=16,` then the value of n is

Options

A. 4
B. 8
C. 2
D. 3

Answer

To solve the equation \( \sqrt{2^n} = 16 \), we can follow these steps:

### Step 1: Rewrite the square root
The square root can be rewritten using exponent notation. Recall that \( \sqrt{x} = x^{1/2} \). Thus, we can rewrite the left side of the equation:
\[ \sqrt{2^n} = (2^n)^{1/2} \]
This simplifies to:
\[ 2^{n/2} \]

### Step 2: Rewrite the right side
Next, we need to express 16 as a power of 2. We know that:
\[ 16 = 2^4 \]

### Step 3: Set the exponents equal
Now we can set the two expressions equal to each other:
\[ 2^{n/2} = 2^4 \]
Since the bases are the same, we can equate the exponents:
\[ \frac{n}{2} = 4 \]

### Step 4: Solve for \( n \)
To find \( n \), we multiply both sides of the equation by 2:
\[ n = 4 \times 2 \]
\[ n = 8 \]

### Final Answer
Thus, the value of \( n \) is:
\[ \boxed{8} \]

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