In what digit will a multiplication string of thirty-five 3s end?

3x3, 3x3x3, and 3x3x3x3 are multiplication strings of two 3s, three 3s, and four 3s respectively.  When each string multiplication is done, 3x3 ends in 9, 3x3x3 ends in 7, 3x3x3x3 ends in 1. In what digit will a multiplication string of thirty-five 3s end?

Considering the pattern of multiplication strings and end-digits:

String	End-Digit
3	3
3x3	9
3x3x3	7
3x3x3x3	1
3x3x3x3x3	3
3x3x3x3x3x3	9

After four 3s, the end-digit pattern repeats itself.
=> string of thirty-five 3s means 35/4 = 8*4+3
=> after 8 four group patterns third iteration which is 7.

A multiplication string of thirty-five 3s will end in 7.