Question

show that 6^n can never end wit digit 0 for any positive integer n

Answer 1

6 to the power n =2×3 but any digits end with zero if 2to the power m and 5 to the power n so this is not ends with zero

Answer 2

let 6^n end with digit zero then the base of 6^n must divisible by2,5 but the base of 6^n only divisible by 2 not 5.
the prime factorization of the base of 6^n contain2,5 but it contain only 2 not 5.
therefore 6^n never end with digit zero.