While I was trying to find out why the first stiefel whitney class of a vector bundle is zero iff its orientable, I figured out that $w_1(Bundle)=w_1(Top\,exterior\,power\,of\,bundle)$ which is zero if the vector bundle is orientable. I did this using the kunneth formula for the exterior power of a direct sum and the formula for the characteristic classes of a tensor product of line bundles.
Question: Given a real vector bundle $E \to B$, is $w_i(E)=w_1(\Lambda^i E)$?