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My dad solved this by turning 7^126 into 49^63 He noticed that 49^2 is 2401, so he split the number into 49^62 x 49 since any number ending in 1 multiplied by itself is 1, he knew that the answer was a number ending in 1 multiplied by a number ending in 9 (49) so the answer is E.
I wrote out the last digits of 7^1, 7^2 etc until they started repeating (7,9,3,1) and then divided 126 by that number (4) to get 31.5 so 31 x 4 = 124 that would be 1 so it is two after- 9
I've never gone to American school, I'm educated in the UK so not sure what the method is in America that may be quicker or easier!
Your method is the one I would use.
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