[tex]\displaystyle\bf\\1)\\a)\\\left[\Big(2^4\Big)^3\times\Big(5^2\Big)^6\right]:10^{12}=\\\\=\Big[2^{4\times3}\times5^{2\times6}\Big]:10^{12}=\\\\=\Big[2^{12}\times5^{12}\Big]:10^{12}=\\\\=(2\times5)^{12}:10^{12}=\\\\=10^{12}:10^{12}=\boxed{\bf1}\\\\\\b)\\2^{16}\times4^{20}:8^{10}=\\\\=2^{16}\times\Big(2^2\Big)^{20}:\Big(2^3\Big)^{10}=\\\\=2^{16}\times2^{2\times20}:2^{3\times10}=\\\\=2^{16}\times2^{40}:2^{30}=2^{16+40-30}=\boxed{\bf2^{26}}[/tex]
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[tex]\displaystyle\bf\\2)\\a)\\2^3+11^1-1^{23}-0^2=8+11-1-0=\boxed{\bf18}\\\\b)\\\\2019\times2018+2019=2019(2018+1)=2019\times2019=\boxed{\bf2019^2=pp}\\\\\\3)\\a)\\4^{102}~cu~2^{200}\\\\\Big(2^2\Big)^{102}~cu~2^{200}\\\\2^{2\times102}~cu~2^{200}\\\\2^{204}~>~2^{200}\\\\\implies~\boxed{\bf4^{102}~>~2^{200}}\\\\b)\\2^{34}~cu~3^{51}\\\\2<3~~si~~34<51\\\\\implies~~\boxed{\bf2^{34}~<~3^{51}}[/tex]
