The word for Authority, as in the Palestinian Authority, is רָשׁוּת (rah-SHOOT). The Palestinian Authority is הָרָשׁוּת הַפַלֶסְטִינִית (hah-fah-less-TEE-neet). I use an f instead of a p because Arabic speakers don't have the p sound - so that when they pronounce this Latin word, Palestine, you'll often hear either Falestine or Balestine.
The plural is רָשׁוּיוֹת (rah-shoo-YOHT), as in, אַל תָּגִידוּ לָרָשׁוּיוֹת (ahl tah-GHEE-doo lah-rah-shoo-YOHT) - don't tell the authorities!
Watch this spoof video (can't see it?) to hear the word in action. Listen and repeat.