A simple algebra

Question

What is the value of1 $0^0$ if I inserted $w=0$? If $0^0=1$ then the answer should be 4th and 5th option only.

Answer 1

There's a wikipedia entry on this. It basically says that depending on your angle of attack (how would you define $0^0$), it's probably either $1$ or undefined.

Answer 2

Yes, you are correct. Usually $$0^0 := 1$$ (note, this is a common definition, $0^0$ is also sometimes defined as $0$ or undefined, but that's rather uncommon)

Your additional task has these solutions in case you want to check: $$w \in (-\infty, 0] \Rightarrow \begin{align*} -3w & \in [0, \infty) \\ 2w + 10 & \in (-\infty, 10] \\ w^4 & \in [0, \infty) \\ w^0 & \in \{1\} \\ -w + 0.5 & \in [0.5, \infty) \end{align*}$$