To simplify the expression \( 714 \cdot 7^{-57^{14} \cdot 7^{-5}} \), we can use the properties of exponents. The particular property we will use is that \( a^m \cdot a^n = a^{m+n} \).
First, rewrite the expression for clarification:
\[ 714 \cdot 7^{-57^{14} \cdot 7^{-5}} = 714 \cdot 7^{-57^{14} - 5} \]
This can be further simplified by combining the exponents. Since \( 714 \) is not an exponent, we cannot combine it with the power of \( 7 \).
The resulting expression in exponential form is:
\[ 714 \cdot 7^{-57^{14} - 5} \]
Thus, the simplified answer is:
\[ 714 \cdot 7^{-57^{14} - 5} \]
However, this form might be the best simplification since \( 714 \) is a numerical coefficient. If you seek to represent it all under a single power of \( 7 \), you could express \( 714 \) in terms of base \( 7 \), if that's necessary, but generally, the current form is acceptable.
Thus the final simplified expression remains:
\[ 714 \cdot 7^{-57^{14} - 5} \]