To simplify the expression \( (4^3 \cdot 27^{-7})^0 \), we can start by applying the property of exponents which states that any non-zero number raised to the power of zero is equal to 1.
Step 1: Apply the zero exponent rule.
\[ (4^3 \cdot 27^{-7})^0 = 1 \]
Since the entire expression is raised to the power of 0, it simplifies to 1.
There is no need to convert or manipulate the terms \( 4^3 \) and \( 27^{-7} \) further, as raising to the zero power simplifies the entire quantity directly to 1.
Thus, the final answer is:
\[ \boxed{1} \]