Quantitative | Re: Cyclicity on the GMAT

for the question 3^7^11:

Given the form 3^a, could you also say that a = 7^11 = (8-1)^11 and thus a = -1^11 = -1

therefore a is one less than a full cycle of 4 (ie 3 more than a multiple of 4) and thus 3^a will result in a units digit of 7

please let me know if this logic is sufficient