Ta có: 55^66 = (55^6)^11 = ((11.5)^6)^11 = (11^6.5^6)^11 = (11^5.11.5^6)^11
66^55 = (66^5)^11 = ((11.6)^5)^11 = (11^5.6^5)^11
Vì 11.5^6 > 6^5 nên 55^66 > 66^55
ta có
\(55^{66}=\left(55^6\right)^{11}=27680640625^{11}\)
\(66^{55}=\left(66^5\right)^{11}=1252332576^{11}\)
Vì 27680640625\(^{11}\)>125233576\(^{11}\)
=> 6655<5566