Math Group

1.(a) If G is a group, gԑG, and the order of g is 60,find the order of g^18 , g^50.(b) If G is a group, gԑG, and the order of g is n,show that the order of g^k, k a positive integer, is equal to n/(g.c.d*k,n).2. Let =Z(n)/nZ, the equivalenceclasses modulo n, with addition + and multiplication * defined in class (a) Consider the group (Z(36),+). Find the orders of theelements [22](36) and [27](36).(b) Consider the group ( defined in class. Find the orders of theelement [2](11) and [3](11)