Exercise $1$: Big$-$O

Consider the following functions:

$n^{1\mathrm{.}5},nlogn,2^n,n!,n^n,\frac{1}{n}$

Rank the listed functions by order of growth., i$.$e$.,$ give an ordering $f_1,f_2,$dots,$f_5$ such that $f_1=O(f_2),f_2=O(f_3),$ and so on$.$ Justify your ordering.