Вычислите [tex](\frac{16^{-\frac{2}{3}}}{\sqrt[4]{0.25}\cdot 2^{-\frac{1}{6}}})^{-1}\cdot\sqrt[5]{32}[/tex]. Created by nikitaaz. algebra-ru

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irkarom

$(\frac{16^{-\frac{2}{3}}}{\sqrt[4]{0.25}\cdot 2^{-\frac{1}{6}}})^{-1}\cdot\sqrt[5]{32}=\frac{\sqrt[4]{0.25}\cdot 2^{-\frac{1}{6}}}{16^{-\frac{2}{3}}}\cdot\sqrt[5]{2^5}= \\ =\frac{\sqrt[4]{0.5^2}\cdot 2^{-\frac{1}{6}}}{2^{4\cdot(-\frac{2}{3})}}\cdot2=\frac{\sqrt{0.5}\cdot 2^{-\frac{1}{6}}}{2^{-\frac{8}{3}}}\cdot2=\frac{\frac{1}{2}^{\frac{1}{2}}\cdot 2^{-\frac{1}{6}}}{2^{-\frac{8}{3}}}\cdot2=\frac{2^{-\frac{1}{2}}\cdot 2^{-\frac{1}{6}}}{2^{-\frac{8}{3}}}\cdot2=\\ \\$

$=2^{-\frac{1}{2}+(-\frac{1}{6})-(-\frac{8}{3})+1}==2^{-\frac{1}{2}-\frac{1}{6}+\frac{8}{3}+1}=2^{\frac{-3-1+16+6}{6}}=2^{\frac{18}{6}}=2^{3}=8$

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