$-5\cdot {\left(-5\right)}^9:{\left(-5\right)}^8={\left(-5\right)}^{1+9-8}={\left(-5\right)}^2=25$

${\left(-3\right)}^7:{\left(-3\right)}^6\cdot {\left(-3\right)}^2={\left(-3\right)}^{7-6+2}={\left(-3\right)}^3=-27$

${\left(0,7\right)}^6\cdot {\left(1\frac{3}{7}\right)}^6-{\left(1,6\right)}^3:{\left(0,8\right)}^3=$ ${\left(0,7\cdot 1\frac{3}{7}\right)}^6-{\left(1,6:0,8\right)}^3={\left(\frac{7}{10}\cdot \frac{10}{7}\right)}^6-2^3=1^6-8=-7$

${\left(0,9\right)}^9\cdot {\left(1\frac{1}{9}\right)}^9-{\left(1,2\right)}^{10}:{\left(1\frac{1}{5}\right)}^{10}=$ ${\left(0,9\cdot 1\frac{1}{9}\right)}^9-{\left(1,2:1\frac{1}{5}\right)}^{10}={\left(\frac{9}{10}\cdot \frac{10}{9}\right)}^9-$ ${\left(1,2:1,2\right)}^{10}=1^9-1^{10}=1-1=0$