[tex]\displaystyle\bf\\6)\\a)\\\Big(5^{17}\cdot5^{18}+7^{23}:7^{15}\Big):\Big(7\cdot7^2\cdot7^5+5^{50}:5^{15}\Big)=\\\\=\Big(5^{17+18}+7^{23-15}\Big):\Big(7^{1+2+5}+5^{50-15}\Big)=\\\\=\Big(5^{35}+7^{8}\Big):\Big(7^{8}+5^{35}\Big)=\\\\=\Big(5^{35}+7^{8}\Big):\Big(5^{35}+7^{8}\Big)=\boxed{\bf1}[/tex]
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[tex]\displaystyle\bf\\b)\\\left[\Big(2^{10}\Big)^{8}+6^5\cdot3^7+2^{3^2}\right]:\left[\Big(2^5\Big)^{16}+6^{12}:2^7+2^9\right]=\\\\=\Big[2^{10\times8}+2^5\cdot3^5\cdot3^7+2^{9}\Big]:\Big[2^{5\times16}+3^{12}\cdot2^{12}:2^7+2^9\Big]=\\\\=\Big[2^{80}+2^5\cdot3^{5+7}+2^{9}\Big]:\Big[2^{80}+3^{12}\cdot2^{12-7}+2^9\Big]=\\\\=\Big[2^{80}+2^5\cdot3^{12}+2^{9}\Big]:\Big[2^{80}+3^{12}\cdot2^{5}+2^9\Big]=\\\\=\Big[2^{80}+2^5\cdot3^{12}+2^{9}\Big]:\Big[2^{80}+2^{5}\cdot3^{12}+2^9\Big]=\boxed{\bf1}[/tex]
