Order the following functions by the most accurate asymptotic notation you learned in this course.

n!, n^2 + n (log n)^10, n^1/3 , (log n)^100, n ^3 , 2^n , 10^( n ) , 2 ^ (log n) , 2 ^(2 log n) , 2 ^( log n) , 128, 128n.

Indicate which functions grow at the same rate (all logarithms are base 2). For example, if you are asked to order n, 2n and 2n^2 , then you answer should be n = (2n), 2n = o(2n^2 ).

Please pay attention to the functions like 10^( n ) since other answers take it as 10 n which is not what I want. Thanks