\frac{64^{\frac{2}{3}}*\sqrt{8}}{0,5^{-4}*\sqrt{4}}-log^2_4 {32}-\frac{1}{2}sin\frac{7\pi}{6}=\frac{\sqrt[3]{64^2}*\sqrt{8}}{(\frac{1}{2})^{-4}*2}-log_4 {32}*log_4 {32}-\frac{1}{2}*(-\frac{1}{2})=\frac{\sqrt[3]{(8^2)^2}*\sqrt{8}}{2^4*2}-\frac{5}{2}*\frac{5}{2}+\frac{1}{4}=\frac{\sqrt[3]{8^4}*\sqrt{8}}{2^5}-\frac{25}{4}+\frac{1}{4}=\frac{8^{\frac{4}{3}}*8^{\frac{1}{2}}}{2^5}-6)=\frac{8^2}{2^5}-6=\frac{(2^3)^2}{2^5}-6=\frac{2^6}{2^5}-6=2-6=-4
sin{\frac{7\pi}{6}}=sin{(\pi+\frac{\pi}{6})}=-sin\frac{\pi}{6}=-\frac{1}{2}cos\frac{4\pi}{3}=cos(\pi+\frac{\pi}{3})=-cos\frac{\pi}{3}=-\frac{1}{2}