# The letters of the Latin Alphabet

Consider all $$26^{26}$$ words of length 26 in the Latin alphabet. Define the weight of a word as $$\dfrac{1}{(k + 1)}$$, where k is the number of letters not used in this word. Find the sum of the weights of all the words in Latin.

If the weight can be represented as $$a^b$$, where $$a$$ is in it's lowest form. That is if the answer is $$8^{66}$$ , $$a$$ is minimised when the answer is rewritten to be $$2^{198}$$. Find $$ab$$.

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