What is the largest n-digit number which is also an exact nth power? For example,the largest 2-digit number which is an exact 2nd power is 81.

Layton Park

Layton Park

Answered question

2022-11-19

What is the largest n-digit number which is also an exact nth power?
For example,the largest 2-digit number which is an exact 2nd power is 81

Answer & Explanation

Claudia Woods

Claudia Woods

Beginner2022-11-20Added 15 answers

You want the largest a n such that 10 n 1 a n < 10 n for a given n
From the right inequality, we have a = 9
Now 10 n 1 9 n is true only when n 21
So, the answer is 9 n for n = 1 , 2 , , 21. For n 22, there is no such number.

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