show work please 215 32768 and the sum of its digits is 3

show work please

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2^2222?

Solution

Given that 2¹⁵ = 32768

        2²²²² = 2^{2220 +2}

                     = 2²²²⁰ 2²                     [ a^m+n = a^m.aⁿ ]

                 = 2^15(148) . 2²

                     = [2^15.2¹⁵...148 times] 2²

Sum of digits = 26 x 148 x 4

                    = 15392