An electric drill is listed for $$507\mathrm{.}92$ less $27\%,19\%,2\%.$

$($a$)$ What is the net price?

$($b$)$ What is the total amount of discount allowed?

$($c$)$ What is the exact single rate of discount that was allowed?

$($a$)$ The net price is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$