To simplify \( 27^{13} \), we can express \( 27 \) as a power of \( 3 \):
\[ 27 = 3^3 \]
Now we can substitute \( 27 \) with \( 3^3 \):
\[ 27^{13} = (3^3)^{13} \]
Using the power of a power property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify it further:
\[ (3^3)^{13} = 3^{3 \cdot 13} = 3^{39} \]
Thus, the simplified form of \( 27^{13} \) is:
\[ 3^{39} \]