Order the following functions by the most accurate asymptotic notation.

n!, n ² + n log¹⁰ n, n ^1/3 , log¹⁰⁰ n, n ³ , 2ⁿ , 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 ).