Question

qual o valor da expressão? 20 pontos

$\frac{ 10^{3}. (10^{2}) ^{-1} . \sqrt{1000} }{ \sqrt{ \frac{1}{100} } . 10^{ \frac{2}{3} } }$

Answer 1

$\frac{10 ^{3}*(10 ^{2} ) ^{-1} * \sqrt{1000} }{ \ \sqrt{ \frac{1}{100} }*10 ^{ \frac{2}{3} } } = \\ \\ \frac{10 ^{3}*10 ^{-2}* \sqrt{10 ^{3} } }{ \sqrt{ \frac{1}{10 ^{2} } } *10 ^{ \frac{2}{3} } } = \\ \\ \frac{10 ^{3}*10 ^{-2}* {(10 ^{3}) ^{ \frac{1}{2} } } }{ \sqrt{ {10 ^{-2} } } *10 ^{ \frac{2}{3} } } = \\ \\ \frac{10 ^{3}*10 ^{-2}* {10 ^{ \frac{3}{2} } } }{ {( {10 ^{-2}) ^{ \frac{1}{2} } } } *10 ^{ \frac{2}{3} } } =$

$\frac{10 ^{3+(-2)+ \frac{3}{2} } }{10 ^{- \frac{2}{2} } +10^{ \frac{2}{3} } } = \\ \\ \frac{10 ^{3-2+ \frac{3}{2} }}{10 ^{-1}*10 ^{ \frac{2}{3} } } = \\ \\ \frac{10 ^{1+ \frac{3}{2} } }{10 ^{-1+ \frac{2}{3} } } = \\ \\ \frac{10 ^{ \frac{2+3}{2} } }{10 ^{ \frac{-3+2}{3} } } = \\ \\ \frac{10 ^{ \frac{5}{2} } }{10 ^{ -\frac{1}{3} } } = \\ \\ 10 ^{ \frac{5}{2} }:10 ^{- \frac{1}{3} } = \\ \\ 10 ^{ \frac{5}{2}-( -\frac{1}{3}) } =$

$10 ^{ \frac{5}{2}+ \frac{1}{3} } = \\ \\ 10 ^{ \frac{15+2}{6} } = \\ \\ 10 ^{ \frac{17}{6} }$