[tex]\displaystyle\\
6)\\
6^2:[4^2-(5\cdot 3^5:15-5^0):2^3]=\\
=6^2:[4^2-(5\cdot3\cdot 3^4:15-5^0):2^3]=\\
=6^2:[4^2-(15\cdot 3^4:15-5^0):2^3]=\\
=6^2:[4^2-(3^4-5^0):2^3]=\\
=6^2:[4^2-(81-1):8]=\\
=6^2:[4^2-80:8]=\\
=6^2:[16-10]=6^2:6= \boxed{6}
[/tex]
[tex]\displaystyle\\
7)\\
~[(3^3+7\cdot 3^7:63):3^3-7^0]\cdot 10^2=\\
=[(3^3+7\cdot 3^2\cdot 3^5:63):3^3-7^0]\cdot 10^2=\\
=[(3^3+7\cdot 9\cdot 3^5:63):3^3-7^0]\cdot 10^2=\\
=[(3^3+63\cdot 3^5:63):3^3-7^0]\cdot 10^2=\\
=[(3^3+3^5):3^3-7^0]\cdot 10^2=\\
=[3^3(1+3^2):3^3-7^0]\cdot 10^2=\\
=[(1+3^2)-7^0]\cdot 10^2=\\
=[(1+9)-1]\cdot 10^2=[10-1]\cdot 10^2=9\cdot 100=\boxed{900}
[/tex]
[tex]\displaystyle\\
8)\\
~[3^4-(2\cdot 2^2\cdot 2^3)^{100}:(2^{150})^4]:4^2=\\
=\Big[3^4-\Big(2^{1+2+3}\Big)^{100}:\Big(2^{150}\Big)^4\Big]:4^2=\\
=\Big[3^4-\Big(2^{6}\Big)^{100}:\Big(2^{150}\Big)^4\Big]:4^2=\\
=\Big[3^4-2^{6\times 100}}:2^{150\times 4}\Big]:4^2=\\
=\Big[3^4-2^{600}}:2^{600}\Big]:4^2=\\
=[3^4-1]:4^2=[81-1]:4^2=80:4^2=80:16 = \boxed{5}[/tex]
