Teaser 2934: Good arraz, Baz!

From The Sunday Times, 16th December 2018 [link]

Baz’s three darts hit the board, scoring different numbers from 1 to 20. “Curious numbers”, said Kaz. Baz looked puzzled. Kaz explained that the first dart’s score to the power of the second dart’s score is a value that contains each numeral 0 to 9 at least once and has the third dart’s score number of digits. Baz only saw that the third dart’s score was the difference between the other two darts’ scores. Kaz wrote the full value on a beer mat. Then Baz put his glass on it and covered most of the value, leaving just the first dart’s score showing to the right and the second dart’s score to the left.

What did each dart score in the order thrown?

[teaser2934]