Question

Вычислите

$(frac{16^{-frac{2}{3}}}{sqrt[4]{0.25}cdot 2^{-frac{1}{6}}})^{-1}cdotsqrt[5]{32}$

Answer 1

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Answer 2

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

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