Adding a Brand taxonomy and displaying it in the single template

I have successfully created a new taxonomy for brands using the code below but can not work out how to display it in the product page.

This is how I ad the custom taxonomy

//hook into the init action and call create_book_taxonomies when it fires
add_action( 'init', 'create_product_taxonomies', 0 );
//add_action('admin_init', 'flush_rewrite_rules'); 

//create two taxonomies, genres and writers for the post type "book"
function create_product_taxonomies()
{
  // Add new taxonomy, make it hierarchical (like categories)
  $labels = array(
    'name' => _x( 'Brands', 'taxonomy general name' ),
    'singular_name' => _x( 'Brand', 'taxonomy singular name' ),
    'search_items' =>  __( 'Search Brands' ),
    'all_items' => __( 'All Brands' ),
    'parent_item' => __( 'Parent Brand' ),
    'parent_item_colon' => __( 'Parent Brands:' ),
    'edit_item' => __( 'Edit Brands' ),
    'update_item' => __( 'Update Brands' ),
    'add_new_item' => __( 'Add New Brand' ),
    'new_item_name' => __( 'New Brand Name' ),
    'menu_name' => __( 'Brands' ),
  );     

  register_taxonomy('product_brand',array('product'), array(
    'hierarchical' => true,
    'labels' => $labels,
    'show_ui' => true,
    'query_var' => true,
    //'rewrite' => true,
    'rewrite' => array( 'slug' => 'brands', 'with_front' => true ),
  ));

function filter_post_type_link($link, $post)
{
    if ($post->post_type != 'product')
        return $link;
  if ($cats = get_the_terms($post->ID, 'product_brand'))
    if ($cats = get_the_terms($post->ID, 'product_brand'))
        $link = str_replace('%product_brand%', array_pop($cats)->slug, $link);
    return $link;
}
add_filter('post_type_link', 'filter_post_type_link', 10, 2);

All good so far and can add my brands as I add a product.

To try to add it to the template I have found the following in meta.php

<?php echo $product->get_categories( ', ', ' <span class="posted_in">'.__('Category:', 'woocommerce').' ', '.</span>'); ?>
	<?php echo $product->get_tags( ', ', ' <span class="tagged_as">'.__('Tags:', 'woocommerce').' ', '.</span>'); ?>

and found the code for the get_categories array in woocommerce_template.php but am not sure what to copy and change to use it.

// NOTE: using child_of instead of parent - this is not ideal but due to a WP bug ( https://core.trac.www.ads-software.com/ticket/15626 ) pad_counts won't work
		$args = array(
			'child_of'		=> $product_category_parent,
			'menu_order'	=> 'ASC',
			'hide_empty'	=> 1,
			'hierarchical'	=> 1,
			'taxonomy'		=> 'product_cat',
			'pad_counts'	=> 1
		);
		$product_categories = get_categories( $args  );

		$product_category_found = false;

		if ( $product_categories ) {

			foreach ( $product_categories as $category ) {

				if ( $category->parent != $product_category_parent )
					continue;

				if ( ! $product_category_found ) {
					// We found a category
					$product_category_found = true;
					echo $before;
				}

				woocommerce_get_template( 'content-product_cat.php', array(
					'category' => $category
				) );

			}

		}

Appreciate your help
charlotteswebpapercraft.com.au

https://www.ads-software.com/extend/plugins/woocommerce/