Let $k^{\prime\prime}$ be an extension field of $k^{\prime}$, and let $|\raisebox{1.72218pt}{.}|^{\prime\prime}$ be a complete absolute value of $k^{\prime\prime}$ as an extension of $|\raisebox{1.72218pt}{.}|^{\prime}$. We set $V_{k^{\prime\prime}}:=V\otimes_{k}k^{\prime\prime}$. Note that $V_{k^{\prime\prime}}=V_{k^{\prime}}\otimes_{k^{\prime}}k^{\prime\prime}$. Let $\|\raisebox{1.72218pt}{.}\|_{k^{\prime\prime}}$ (resp. $\|\raisebox{1.72218pt}{.}\|_{k^{\prime},k^{\prime\prime}}$) be a norm of $V_{k^{\prime\prime}}$ obtained by the scalar extension of $\|\raisebox{1.72218pt}{.}\|$ on $V$ (resp. the scalar extension of $\|\raisebox{1.72218pt}{.}\|_{k^{\prime}}$ on $V_{k^{\prime}}$). Then $\|\raisebox{1.72218pt}{.}\|_{k^{\prime\prime}}=\|\raisebox{1.72218pt}{.}\|_{k^{\prime},k^{\prime\prime}}$.