Suppose W1,…,WmW_1,\dots,W_mW1,…,Wm are vector spaces. Prove that L(V,W1×⋯×Wm)\mathcal L(V,W_1\times\dots\times W_m)L(V,W1×⋯×Wm) and L(V,W1)×⋯×L(V,Wm)\mathcal L(V,W_1)\times\dots\times\mathcal L(V,W_m)L(V,W1)×⋯×L(V,Wm) are isomorphic vector spaces.
TODO