Question

(UFMG) O valor de m = $( \sqrt{ (-3)^{2} } - \frac{1}{0.444...}) ^{ \frac{-3}{2} } × \frac{3}{ \sqrt[4]{ 2^{8} } }$ , é:
resposta:$\frac{2}{ \sqrt{3} }$

Answer 1

$( \sqrt{(-3)^2}- \frac{1}{0,444...} )^{ -\frac{3}{2} } \frac{3}{ \sqrt[4]{2^8} } \ \ \ \ \ \ \ ( 0,444... = \frac{4}{9} )\\ \\ ( \sqrt{9}- \frac{1}{ \frac{4}{9} } )^{ -\frac{3}{2} } \frac{3}{(2)^{ \frac{8}{4} } } \ \ \ \ \ \ \ (\sqrt[n]{x^p} =x^{ \frac{p}{n} }) \\ \\ ( 3- 1.\frac{9}{4} } )^{ -\frac{3}{2} } \frac{3}{(2)^{ 2 } } \\ \\ ( \frac{12-9}{4} } )^{ -\frac{3}{2} } \frac{3}{4 } } \\ \\ ( \frac{3}{4} } )^{ -\frac{3}{2} } \frac{3}{4 } } \\ \\ (\frac{3}{4})^{(- \frac{3}{2} + 1 )}$
$(\frac{3}{4})^{- \frac{1}{2}} = (\frac{4}{3}) ^{ \frac{1}{2} }= \sqrt{ \frac{4}{3} } = \frac{ \sqrt{4} }{ \sqrt{3} }= \frac{2}{ \sqrt{3} }$

As partes que eu não expliquei direito pode me perguntar se precisar. rsrs
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$x^p*x^q=x^{p+q}$