Question

Explain why (–4x)0 = 1, but –4x0 = –4.

Answer 1

I assume you're asking why:
\[(-4x)^0=1\] whilst \[-4x^0=-4\]
and the answer is that anything to the 0 is defined as 1.
and the order of operations:
(-4x)^0 is saying the variable and coefficient are to the 0 while
-4x^0 is only taking the variable to the 0 which means:
\[-4x^0\implies-4(1)=-4\]

Answer 2

what agreen said. for the same reason that
\[2\times 3^2=2\times 9=18\] but
\[(2\times 3)^2=6^2=36\]