$a)$  

$a^{12}\cdot b^8\cdot c^2\cdot a^{15}\cdot b^{10}\cdot c^{20}\cdot abc=$  

$=a\cdot a^{12}\cdot a^{15}\cdot b\cdot b^8\cdot b^{10}\cdot c\cdot c^2\cdot c^{20}=$  

$=a^{1+12+15}\cdot b^{1+8+10}\cdot c^{1+2+20}=$  

$=a^{28}{b}^{19}{c}^{23}$  

 

$b)$  

$m^7\cdot {\left(-n\right)}^2\cdot m^5\cdot {\left(-n\right)}^{12}\cdot m\cdot \left(-n\right)=$  

$=m\cdot m^5\cdot m^7\cdot \left(-n\right)\cdot {\left(-n\right)}^2\cdot {\left(-n\right)}^{12}=$  

$=m^{1+5+7}\cdot {\left(-n\right)}^{1+2+12}=$  

$=m^{13}\cdot {\left(-n\right)}^{15}$  

 

$c)$  

$\left(a^{12}:a^8\right)\cdot \left(a^{15}:a^7\right)\cdot \left(a^{20}:a^{17}\right)=$  

$=a^{12-8}\cdot a^{15-7}\cdot a^{20-17}=$  

$=a^4\cdot a^8\cdot a^3=$  

$=a^{4+8+3}=$  

$=a^{15}$  

 

$d)$  

$n^{30}:\left[n^{15}\cdot \left(n^{10}:n^8\right):\left(n^3\cdot n^{10}\right)\right]=$  

$=n^{30}:\left[n^{15}\cdot n^{10-8}:n^{3+10}\right]=$  

$=n^{30}:\left[n^{15}\cdot n^2:n^{13}\right]=$  

$=n^{30}:n^{15+2-13}=$  

$=n^{30}:n^4=$  

$=n^{30-4}=$  

$=n^{26}$