how to return data php to ajax

i need a simple help about return data php to ajax .
didn't understand how to get data from php by ajax.

here is my javascript code :

$('#value').on('keyup', function(event){
   event.preventDefault();
   var form_data = $(this).serialize();
   var sending = $("#sending").val();
   var value = $("#value").val();
   var recevied = $("#recevied").val();
   $.ajax
   ({
       type: "POST",
       //async: true,
       dataType : 'json',
       url: "",
       data: {_token:"", sending:sending,value:value,recevied:recevied}
   }).done( function(data){
     //swal("Good job!", "Your personal information has been successfully updated!", "success")
        $("#mainvalue").val(data)
        console.log('Ajax was Successful!')
        console.log(data)
   }).fail(function(xhr, textStatus, error){
       console.log(textStatus)
       console.log(error)
   });

});

here is my php code :-

public function index(Request $request)
{
  $sending = $request->get('sending');
  $value = $request->get('value');
  $recevied = $request->get('recevied');
  $relations = DB::table('tbl_relations')
              ->where('exid1',$sending)
              ->where('exid2',$recevied)
              ->select()
              ->first();
  if ($relations != null) {
    $rate = $relations->exrate2;
    $mainvalue = $sending * $rate;
    return $rate;
  }else{
    return $request->all();
  }

}

i want restore $rate value into #mainvalue

via Chebli Mohamed