`sqrt((13)^(4))=?`

Options

A. 520
B. 169
C. 28561
D. 14280

Answer

To solve the question \( \sqrt{(13)^{4}} \), we can follow these steps:

### Step 1: Rewrite the square root
The square root can be expressed as an exponent of \( \frac{1}{2} \). Therefore, we can rewrite the expression as:
\[ \sqrt{(13)^{4}} = (13^{4})^{\frac{1}{2}} \]

### Step 2: Apply the power of a power rule
Using the power of a power rule, which states that \( (a^{m})^{n} = a^{m \cdot n} \), we can simplify the expression:
\[ (13^{4})^{\frac{1}{2}} = 13^{4 \cdot \frac{1}{2}} = 13^{2} \]

### Step 3: Calculate \( 13^{2} \)
Now we need to calculate \( 13^{2} \):
\[ 13^{2} = 13 \times 13 = 169 \]

### Final Answer
Thus, the value of \( \sqrt{(13)^{4}} \) is:
\[ \boxed{169} \]

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