iRule assistance

At its simplest...

when HTTP_REQUEST {
    switch -glob -- [string tolower [HTTP::uri]] {
        "/thing-a/*" { pool "apiPoolA" }
        "/thing-b/*" { pool "apiPoolB" }
        default { HTTP::respond 400 content "Unsupported URI" noserver }
    }
}

i.e., in the HTTP_REQUEST event, read the URI, convert it to lower-case (for easier comparing) and compare it to one or more simple patterns. 

If the URI starts with /thing-a/, forward to one specific backend pool; if it starts with /thing-b/, forward to another.

If the URI does not match either of those patterns, respond with a basic HTTP error message.

Note that, to the BIGIP, the term "URI" means "the path and querystring".  If you actually want just the path, try [HTTP::path]; if you want the hostname, try [HTTP::host]; or if you want both, consider "[HTTP::host][HTTP::uri]".

If you need the scheme (i.e. if it is HTTP or HTTPS), it can be a little trickier.  Possibly [expr { [PROFILE::exists clientssl] ? "https" : "http" }].