Question

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

Answer 1

anything (except 0) to the 0th power is always 1

so that's why x^0 = 1

Answer 2

when it comes to (-4x)^0, you can think of -4x as z (ie let z = -4x) to get z^0 = 1

so that's why (-4x)^0 = 1

Answer 3

\[(-4x)^0=(-1)^0(4)^0(x^0)=1\cdot1\cdot1=1\]
whereas
\[-4x^0=-4\cdot1=-4~~~~~~~\text{(the exponent only applies to the }x)\]