First, we need to simplify the expressions, as follows:
[tex]\begin{gathered} \sqrt[]{100}=10 \\ \sqrt[]{9}=3 \\ 2^2=4 \\ \sqrt[]{4}=2 \\ -4^2=-16 \\ 0^2=0 \\ \sqrt[]{1}=1 \\ 3^2=9 \\ (-4)^2=16 \end{gathered}[/tex]Then, the ordered list is:
[tex]\begin{gathered} -16,0,1,2,3,4,9,10,16 \\ or \\ -4^2,0^2,\sqrt[]{1},\sqrt[]{4},\sqrt[]{9},2^2,3^2,\sqrt[]{100},(-4)^2 \end{gathered}[/tex]