To simplify \( 13 \sqrt{27} \), we first simplify \( \sqrt{27} \).
The number \( 27 \) can be factored as:
\[ 27 = 9 \times 3 = 3^2 \times 3 \]
Thus, we can simplify \( \sqrt{27} \):
\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3 \sqrt{3} \]
Now, substituting this back into the expression \( 13 \sqrt{27} \):
\[ 13 \sqrt{27} = 13 \times 3 \sqrt{3} = 39 \sqrt{3} \]
So, \( 13 \sqrt{27} \) simplifies to \( 39 \sqrt{3} \).
Therefore, the expression \( 39 \sqrt{3} \) is the simplified form, and it is not equal to \( 16 \sqrt{339} \) or any other expression provided.
In conclusion, the simplified expression is:
\[ 39 \sqrt{3} \]