since we only need to find the largest of the 5 numbers, we just compare them 2-by-2 in a knock-out competition.

note that if a>b and n>0, then a^n > b^n,
and vice versa.

compare 2^30 and 4^14 ...
since 4^14 = 2^28 < 2^30, so 2^30 wins round 1.

compare 3^19 and 9^10 ...
since 9^10 = 3^20 > 3^19, so 9^10 wins round 2.

compare 2^30 and 6^12 ...
take the 6th root of both numbers, we have ...
2^5 = 32 and 6^2 = 36, so 6^12 wins round 3.

compare 6^12 and 9^10 (=3^20) ...
take the 4th root of both numbers, we have ...
6^3 = 216 and 3^5 = 243, so 9^10 wins round 4.

therefore (E) 9^10 is the overall winner of the knock-out competition !!!