[tex]a)\\(\frac{1}{7})^{2}\cdot14^{2}-10^{5}\cdot(\frac{1}{5})^{5} = (\frac{1}{7}\cdot14)^{2}-(10\cdot\frac{1}{5})^{2} = 2^{2}-2^{5} = 4 - 32 = -28\\\\\\b)\\35^{2}:(-7)^{2}+(-6)^{3}:(-2)^{3} = (35:(-7))^{2}+(-6:(-2))^{3} =(-5)^{2}+3^{3} =\\\\= 25+27 = 52[/tex]
[tex]c)\\4^{2}\cdot(\frac{1}{4})^{2}-(\frac{1}{5})^{3}\cdot5^{3} = (4\cdot\frac{1}{4})^{2}-(\frac{1}{5}\cdot5)^{3} = 1^{2}-1^{3} = 1-1 = 0[/tex]
[tex]d)\\(\frac{3}{7})^{3}:(-\frac{6}{7})^{3}-15^{4}:(-5)^{4}=(\frac{3}{7}\cdot(-\frac{7}{6}))^{3}-(15\cdot(-\frac{1}{5})^{4} = (-\frac{1}{2})^{3}-(-3)^{4} =\\\\= -\frac{1}{8}-81 = -81\frac{1}{8}[/tex]
