Taxonomy dropdown metabox in the back-end

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I had the same question.

You use the remove_meta_box functions mentioned in a previous answer, but you have two options: tagsdiv-{$tax_name} for non-hierarchical taxonomies and {$tax_name}div for hierarchical taxonomies (like categories). So in your case:

 remove_meta_box('tagsdiv-brands', 'post', 'normal');
 remove_meta_box('brandsdiv', 'post', 'normal');