Getting the first parent of a hierarqui category

How get avô this hierarqui category:

avô
-mae
--filho

It always give me the last child :

<?php 

    $product_cats = wp_get_post_terms( get_the_ID(), 'product_cat' );

    $single_cat = array_shift( $product_cats ); 

    echo $single_cat->slug;

?>

Result: filho

Must obtain the category avô

UPDATE:

$product_cats return:

Array
(
    [0] => stdClass Object
        (
            [term_id] => 16
            [name] => Display
            [slug] => display-co-ele
            [term_group] => 0
            [term_taxonomy_id] => 16
            [taxonomy] => product_cat
            [description] => 
            [parent] => 7
            [count] => 2
            [filter] => raw
        )

)