These questions are of interest because only partial answers have been given.
When k=2-if N2 is a palindrome then N is often, but not always, a
palindrome. When k=3-the only known palindromic cube without a palindromic cube
root is 10,662,526,601, but there may be others yet undiscovered. When k=4 -all
known palindromic fourth powers have fourth roots that are palindromes, but what
about those that are yet unknown; When k=5 -this one's a little harder as there
are no known palindromes that can be written in the form N5. Clearly
the answers to these questions are a proper subject for creative