# First nonzero Stiefel-Whitney class

In Milnor-Stasheff's Characteristic Classes, one of the problems says that the smallest nonzero $$w_i(E)$$ happens when $$i$$ is a power of 2 in the case where $$w(E) = 1$$.

That the first nonzero stiefel-whitney class is always given by a power of two. Is this true or does it only happen when the total sw class is 1? Where can I find a clear explanation?

If not, I am wondering if there are any conditions on manifolds that would tell us when $$w(E) = 1$$ or not. In particular, I am interested in closed, orientable manifolds.