[tex]\displaystyle\bf\\1)\\\\\left(\frac{2}{3}\right)^{5}\times\left(\frac{2}{3}\right)^{8}:\left(\frac{2}{3}\right)^{10}=\left(\frac{2}{3}\right)^{5+8-10}=\left(\frac{2}{3}\right)^{3}=\frac{2^3}{3^3}=\frac{8}{27}\\\\\\2)\\\\\left(\frac{3}{7}\right)^{2}:\left(\frac{3}{7}\right)^{0}+\frac{1}{7}:\frac{3}{7}=\left(\frac{3}{7}\right)^{2-0}+\frac{1}{7}\times\frac{7}{3}=\\\\\\=\frac{3^2}{7^2}+\frac{1}{7}\times\frac{7}{3}=\frac{^{3)}9}{49}+\frac{^{49)}1}{3}=\frac{27+49}{49\times3}=\frac{76}{147}[/tex]
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[tex]\displaystyle\bf\\3)\\\\\frac{1}{2}\times\left(\frac{2}{3}\right)^3+\frac{1}{6}=\frac{1}{2}\times\frac{2^3}{3^3}+\frac{1}{6}=\frac{1}{2}\times\frac{8}{27}+\frac{1}{6}=\\\\=\frac{^{2)}4}{27}+\frac{^{9)}1}{6}=\frac{8+9}{54}=\frac{17}{54}[/tex]
