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If $\overline{\mathbb{Q}}$ denotes the algebraic closure of $\mathbb{Q}$, and $n$ is a positive integer, why is $\mathbb{Q}^n \otimes_\mathbb{Q} \overline{\mathbb{Q}} = \overline{\mathbb{Q}}^n$?

I.e. why is the tensor product over $\mathbb{Q}$ of $\mathbb{Q}^n$ with the algebraic closure of $\mathbb{Q}$ isomorphic to the algebraic closure of $\mathbb{Q}$ to the $n$?

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    Next time, please kindly make your posts human readable by using latex.2011-04-25

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