Biggest a^b for a+b=n, n<=100

['0^0',
 '1^0',
 '2^0',
 '2^1',
 '2^2',
 '3^2',
 '3^3',
 '3^4',
 '4^4',
 '4^5',
 '4^6',
 '4^7',
 '5^7',
 '5^8',
 '5^9',
 '6^9',
 '6^10',
 '6^11',
 '6^12',
 '7^12',
 '7^13',
 '7^14',
 '7^15',
 '8^15',
 '8^16',
 '8^17',
 '8^18',
 '9^18',
 '9^19',
 '9^20',
 '9^21',
 '10^21',
 '10^22',
 '10^23',
 '10^24',
 '10^25',
 '11^25',
 '11^26',
 '11^27',
 '11^28',
 '12^28',
 '12^29',
 '12^30',
 '12^31',
 '12^32',
 '13^32',
 '13^33',
 '13^34',
 '13^35',
 '14^35',
 '14^36',
 '14^37',
 '14^38',
 '14^39',
 '15^39',
 '15^40',
 '15^41',
 '15^42',
 '16^42',
 '16^43',
 '16^44',
 '16^45',
 '16^46',
 '17^46',
 '17^47',
 '17^48',
 '17^49',
 '17^50',
 '18^50',
 '18^51',
 '18^52',
 '18^53',
 '18^54',
 '19^54',
 '19^55',
 '19^56',
 '19^57',
 '19^58',
 '20^58',
 '20^59',
 '20^60',
 '20^61',
 '20^62',
 '21^62',
 '21^63',
 '21^64',
 '21^65',
 '21^66',
 '22^66',
 '22^67',
 '22^68',
 '22^69',
 '22^70',
 '23^70',
 '23^71',
 '23^72',
 '23^73',
 '23^74',
 '24^74',
 '24^75',
 '24^76']