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$1) ( 2^{10} )^3:2^{33} = 2^{30-33}=2^{-3}=1/8=0,125 \\ 2) \frac{(7^{-7}-7^{-6})}{7-12} =\frac{(7^{-6}*7^{-1}-7^{-6})}{-5}=\frac{(7^{-6}(7^{-1}-1))}{-5} = \\ \frac{-6*7^{-6}}{7*5}= 1,2*7^{-7} \\ 3)8 \sqrt{3}*\sqrt{2}* 2 \sqrt{6} =16 \sqrt{36}=96 \\ 4) ( \sqrt{86}+1)^2 = 87+2 \sqrt{86} = 105,54.. \\ 5) \sqrt{24} ; 2 \sqrt{8} ; 6 ; \sqrt{8}+ \sqrt{10} =\ \textgreater \ \\ \sqrt{24} ; \sqrt{32} ; \sqrt{36} ; \sqrt{35} =\ \textgreater \ \sqrt{24} \ \textless \ \sqrt{32} \ \textless \ \sqrt{35} \ \textless \ \sqrt{36}$
$6)8 ; 2 \sqrt{14} ; 6 \sqrt{2} =\ \textgreater \ \sqrt{64} ; \sqrt{56}; \sqrt{72} =\ \textgreater \ \\ \sqrt{56} \ \textgreater \ \sqrt{64}\ \textgreater \ \sqrt{72} =\ \textgreater \ 6 \sqrt{2} ; 8 ; 2 \sqrt{14}$