$3\mathrm{.}2[2$ point, $0\mathrm{.}5$ each$]$ What are the big$-$O

notations for the following functions?

$(1)n^{3}log(3n)+2n^4+3n^2+127$

$(2)\sqrt[\phantom{2}]{2n}+30log(4n{)}^2+27n-3$

$(3)(n+1)!+2^n$

$(4)\sqrt[3]{n^2}+3nlo{g}^2(2n)+4n^{\frac{6}{7}}$