RewriteEngine On
RewriteBase /example/

# Rewrite api/v1/* to /example/router.php
RewriteRule ^api/v1/(.*)$ router.php [L,QSA]

# Leave other requests unchanged
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ $1 [L]