Feferman-Vaught theorem and Term Powers

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In an example of usage of quantifier elimination in wikipedia, it briefly mentions Feferman-Vaught theorem and Term Powers, but I am finding little information on what these are. Can anyone explain what Feferman-Vaught theorem and Term Powers are?

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There's a section on the Feferman-Vaught theorem on page 458 of Hodges' "Model Theory" :)