We start with the expression:
\[ \left(14^3 \times 27^{-7}\right)^0 \div 3^4 \]
According to the property of exponents, any non-zero number raised to the power of zero equals 1:
\[ \left(14^3 \times 27^{-7}\right)^0 = 1 \]
Now we can substitute that back into the expression:
\[ 1 \div 3^4 \]
Calculating \(3^4\):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]
Now substitute that into the expression:
\[ 1 \div 81 = \frac{1}{81} \]
So the final simplified expression is:
\[ \frac{1}{81} \]
Thus, the answer is:
\[ \frac{1}{81} \]