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Question 1

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Question 2

$\frac{4^{-0.5}* 8^{\frac{4}{5}}}{(\sqrt[5] 2)^2}*(0.001^{\frac{1}{3}}*10^2)^{-\frac{1}{2}}=\\ \frac{(2^2)^{-0.5}* (2^3)^{\frac{4}{5}}}{2^\frac{2}{5}} *(\sqrt[3]{0.001}*10^2)^{-\frac{1}{2}}=\\ \frac{2^{2*(-0.5)}* 2^{3*\frac{4}{5}}}{2^\frac{2}{5}} *(0.1*100)^{-\frac{1}{2}}=\\ \frac{2^{-1}* 2^{\frac{12}{5}}}{2^\frac{2}{5}} *10^{-\frac{1}{2}}=\\$

$2^{-1+\frac{12}{5}-\frac{2}{5}}*(\frac{1}{10})^{\frac{1}{2}}=\\ 2^{-1+2}*(\frac{1}{10})^{\frac{1}{2}}=\\ 2^{1}*(\frac{1}{\sqrt{10}})=\\(\frac{2\sqrt{10}}{10})=0.2 \sqrt {10}$

$(0.36ac^{\frac{2}{3}})^{\frac{1}{2}} * (\frac{1}{125}a^{\frac{3}{4}}c)^{-\frac{1}{3}}=\\ \sqrt{0.36} a^{\frac{1}{2}}c^{\frac{2*1}{3*2}} * (125a^{\frac{-3}{4}}c^{-1})^{\frac{1}{3}}=\\ 0.6a^{\frac{1}{2}}c^{\frac{1}{3}} * \sqrt[3]{125}a^{\frac{-3*1}{4*3}}c^{-\frac{1}{3}}=\\ 0.6a^{\frac{1}{2}-\frac{1}{4}}c^{\frac{1}{3}-\frac{1}{3}} * 5=\\ 3a^{\frac{1}{2}}=3\sqrt a$

$\frac {27^{-\frac{1}{4}}*9^{1.5}}{ (\sqrt[8] 3)^2}*(0.04^{\frac{1}{2}}*5^4)^{-\frac{1}{3}}=\\$

$\frac {3^{-\frac{3}{4}}*3^{2*1.5}}{3^{\frac{1}{4}}}*(0.2*5^4)^{-\frac{1}{3}}= \\ \frac {3^{-\frac{3}{4}}*3^{3}}{3^{\frac{1}{4}}}*(5^3)^{-\frac{1}{3}}= \\ 3^{-\frac{3}{4}+3-\frac{1}{4}}*5^{-\frac{1}{3}*3}=\\ 3^{2}*5^{-1}=\\9*\frac{1}{5}=\frac{9}{5}=1.4$

$(0.27a^2c)^{\frac{1}{3}}(\frac{1}{25}ac^{\frac{2}{3}})^{-\frac{1}{2}}=\\ \sqrt[3]{0.27}a^{\frac{2*1}{3}}c^{\frac{1}{3}}\sqrt{25}a^{-\frac{1}{2}}c^{\frac{-2*1}{3*2}}=\\ 3\sqrt[3]{0.01}a^{\frac{2}{3}}c^{\frac{1}{3}} *5a^{-\frac{1}{2}}c^{\frac{-1}{3}}=\\ 15\sqrt[3]{0.01}a^{\frac{2}{3}-\frac{1}{2}}c^{\frac{1}{3}-\frac{1}{3}}=\\ 15\sqrt[3]{0.01}a^{\frac{1}{6}}=\\$