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Problem 56

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Powerful Digit Sum

A googol (${10}^{100}$) is a massive number: one followed by one-hundred zeros; ${100}^{100}$ 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?

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幂的数字和

一古戈尔（${10}^{100}$）是一个巨大的数字：一后面跟着一百个零。${100}^{100}$则更是无法想像地巨大：一后面跟着两百个零。然而，尽管这两个数如此巨大，各位数字和却都只有$1$。

对于$a,b<100$，考虑所有能表示为$a^b$的自然数，其中最大的各位数字和是多少？

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