To simplify the expression \( 27^{13} \), we can rewrite 27 as \( 3^3 \). Thus, we have:
\[ 27^{13} = (3^3)^{13} \]
Using the power of a power property, which states that \( (a^m)^n = a^{m \cdot n} \), we can simplify it further:
\[ (3^3)^{13} = 3^{3 \cdot 13} = 3^{39} \]
Therefore, the simplified form of \( 27^{13} \) is:
\[ 3^{39} \]