Why the binomial theorem doesn't work at $ k=0$?

Question

For an expansion $(1+x)^k$, you get $0$ when you let $k=0$ and apply the Binomial Theorem. However, the answer from my book is $1$. I'm either missing something or my book isn't telling me when the theorem does and doesn't work. Please clear this up for me!

Answer 1

It works:

$$(1+x)^0=\sum_{k=0}^0\binom0k1^kx^{0-k}=\binom001^0x^0=1\cdot1\cdot1=1\;.$$

I suspect that what you’re missing is the fact that $\binom00=1$.