Each stroke of a pump removes 8.2% of the remaining air from a container. What percent of the air remains after 50 strokes?

I originally thought this was simple, use the formula

where

and

substituting in these values i get

and therefore ~1.51%

however, the solution in my textbook shows the intermediary step to be

and final solution as

Which brings me to my main question: Could somebody explain to me why the textbook's solution shows instead of ? Is it something to do with ? a mistake in the book? or something else?

thanks in advance