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Prob­lem

A googol (10¹⁰⁰) is a mas­sive num­ber: one fol­lowed by one-hundred zeros; 100¹⁰⁰ is almost unimag­in­ably large: one fol­lowed by two-hundred zeros. Despite their size, the sum of the dig­its in each num­ber is only 1.

Con­sid­er­ing nat­ural num­bers of the form, a^b, where a, b < 100, what is the max­i­mum dig­i­tal sum?

Solu­tion