## Powerful digit counts

### Problem 63

The 5-digit number, 16807=7^{5}, is also a fifth power. Similarly, the 9-digit number, 134217728=8^{9}, is a ninth power.

How many *n*-digit positive integers exist which are also an *n*th power?

The 5-digit number, 16807=7^{5}, is also a fifth power. Similarly, the 9-digit number, 134217728=8^{9}, is a ninth power.

How many *n*-digit positive integers exist which are also an *n*th power?