$a)-5a\cdot 7a=-35a^2$

$b)c^2{b}^2{a}^2\cdot \frac{1}{2}=\frac{1}{2}{a}^2{b}^2{c}^2$ $b)c^2{b}^2{a}^2\cdot \frac{1}{2}=\frac{1}{2}{a}^2{b}^2{c}^2$

$c){\sout{11}}^1{y}^3{x}^2{y}^2\cdot \frac{1}{{\sout{22}}^2}=\frac{1}{2}{x}^2{y}^5$

$d)-abccbaabc=-a^3{b}^3{c}^3$

$e)\sqrt{8}{x}^7{y}^{6}x{y}^2=\sqrt{4\cdot 2}{x}^{7}x{y}^6{y}^2=2\sqrt{2}{x}^8{y}^8$

$f)-1,4a\cdot \frac{1}{7}a\left(-1,4a\right)\cdot \frac{1}{7}a=\left(-1,4\cdot \left(-1,4\right)\cdot \frac{1}{7}\cdot \frac{1}{7}\right)a^4=\left(\frac{{\sout{14}}^2}{10}\cdot \frac{{\sout{14}}^2}{10}\cdot \frac{1}{\sout{7}\cdot \sout{7}}\right)a^4=\frac{4}{100}{a}^4$