Question

if "n" is a natural number, then 6 to the power n minus 5 to the power n always ends with what?

Answer 1

if n  is a natural number
then 6 to the power n - 5 to the power n will end with 1
Example-(1)    6 to the power 1 - 5 to the power 1 ends with 1
(2)       6 to the power 2 - 5 to the power 2 =36-25 =11 which ends with 1 .
                    
  

Answer 2

$6^n-5^n=(6-5)(6^{n-1}+6^{n-2}(5)+...+6(5^{n-2})+5^{n-1})=(6^{n-1}+6^{n-2}(5)+...6(5^{n-2})+5^{n-1})$
therefore
so $6^n-5^n=(6^{n-1}+6^{n-2}(5)+...+6(5^{n-2})+5^{n-1})$