Let's carefully evaluate the given mathematical expression step by step:
[tex]\[
\left( \frac{x^2 + (-y^4) \cdot 2^6 - 4 \cdot (7 \cdot 6)}{7 \cdot (x - 26 + 4)} \right)^0
\][/tex]
First, let's analyze the exponent:
The expression is raised to the power of [tex]\(0\)[/tex].
Step 1: Any number or expression (assuming it is not zero in the denominator) raised to the power of 0 is 1.
Therefore, the expression inside the parentheses does not need to be simplified for the final evaluation of the power [tex]\(0\)[/tex].
Step 2: Applying the power of [tex]\(0\)[/tex]:
[tex]\[
\left( \frac{x^2 + (-y^4) \cdot 2^6 - 4 \cdot (7 \cdot 6)}{7 \cdot (x - 26 + 4)} \right)^0 = 1
\][/tex]
Thus, the final value of the given expression is:
[tex]\[
1
\][/tex]