### Instruction: Find the smallest positive integer that is both an integer power of 11 and is not a palindrome.### Response: A palindrome is a number that reads the same forward and backward, like 121 or 313.
So I want to find the smallest power of 11 that is not a palindrome.
I know that 11^0 = 1, 11^1 = 11, and 11^2 = 121 are all palindromes.
So I need to check 11^3 and see if it is a palindrome or not.
I can use a calculator or do the multiplication by hand.
I get 11^3 = 1331.
This is also a palindrome, so I need to keep going.
I check 11^4 and get 14641.
This is still a palindrome, so I need to check 11^5.
I get 11^5 = 161051.
This is not a palindrome, because the first and last digits are different.
So I have found the smallest power of 11 that is not a palindrome.