I am having a little trouble understanding little-o notation when it appears in the exponent. I understand the $2^{3k} \notin 2^{o(k)}$ since $2^{o(k)}$ is not an upper bound for $2^{3k}$. But how can I prove\refute a comparison among two $o$ notations?
Is $2^{o(k)} = 2^{o(3k)}$?