$a)$  

$\frac{2^{78}\cdot 4^{36}-3\cdot 8^{36}:4^8\cdot {16}^{15}}{22\cdot {\left[{\left({32}^3\right)}^2\cdot 2^7\right]}^4}=$  

$=\frac{2^{78}\cdot {\left(2^2\right)}^{36}-3\cdot {\left(2^3\right)}^{36}:{\left(2^2\right)}^8\cdot {\left(2^4\right)}^{15}}{22\cdot {\left[{\left({\left(2^5\right)}^3\right)}^2\cdot 2^7\right]}^4}=$  

$=\frac{2^{78}\cdot 2^{72}-3\cdot 2^{108}:2^{16}\cdot 2^{60}}{22\cdot {\left[{\left(2^{15}\right)}^2\cdot 2^7\right]}^4}=$  

$=\frac{2^{150}-3\cdot 2^{108-16+60}}{2\cdot 11\cdot {\left[2^{30}\cdot 2^7\right]}^4}=$  

$=\frac{2^{150}-3\cdot 2^{152}}{2\cdot 11\cdot {\left[2^{37}\right]}^4}=$  

$=\frac{2^{150}-3\cdot 2^{152}}{2\cdot 11\cdot 2^{148}}=$  

$=\frac{2^{149}\cdot 2-3\cdot 2^{149}\cdot 2^3}{11\cdot 2^{149}}=$  

$=\frac{\sout{2^{149}}\cdot \left(2-3\cdot 2^3\right)}{11\cdot \sout{2^{149}}}=$  

$=\frac{2-3\cdot 8}{11}=$  

$=\frac{2-24}{11}=$  

$=\frac{-22}{11}=$  

$=-2$  

 

$b)$  

$\frac{8^{12}\cdot {\left(5^2\right)}^{17}+{10}^{35}}{{\left({10}^8\right)}^4\cdot \left(-1\right)+{\left(5^4\right)}^8\cdot {\left(2^7\right)}^5}=$  

$=\frac{{\left(2^3\right)}^{12}\cdot 5^{34}+{\left(2\cdot 5\right)}^{35}}{{10}^{32}\cdot \left(-1\right)+5^{32}\cdot 2^{35}}=$  

$=\frac{2^{36}\cdot 5^{34}+2^{35}\cdot 5^{35}}{-{\left(2\cdot 5\right)}^{32}+5^{32}\cdot 2^{35}}=$  

$=\frac{2^{32}\cdot 2^4\cdot 5^{32}\cdot 5^2+2^{32}\cdot 2^3\cdot 5^{32}\cdot 5^3}{-2^{32}\cdot 5^{32}+5^{32}\cdot 2^{32}\cdot 2^3}=$  

$=\frac{\sout{2^{32}\cdot 5^{32}}\cdot \left(2^4\cdot 5^2+2^3\cdot 5^3\right)}{\sout{2^{32}\cdot 5^{32}}\cdot \left(-1+2^3\right)}=$  

$=\frac{16\cdot 25+8\cdot 125}{-1+8}=$  

$=\frac{400+1000}{7}=$  

$=\frac{1400}{7}=$  

$=200$