Demonstrate why this is the case - if one examines the rows

Question

Question 1

Problem

If one examines the rows of Pascal's triangle, one can spot that the numbers in the row correspond to the digits of the powers of 11. For instance, the row zero is 1 = 11⁰, row one is 11 = 11¹, row two is 121 = 11², row three is 1331 = 11³, and so forth. Even when it appears as if the pattern breaks with row 5 (1, 5, 10, 10, 5, 1), by carrying the one from each 10 over, we end up with 1, 6, 1, 0, 5, 1; or 161; 051 = 11⁵.

Using the Binomial Theorem, demonstrate why this is the case.