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\(C=\left(1-2-3-4\right)+...+\left(197-198-199-200\right)\)
=-8x25=-200
\(D=-\left(11+13+...+99\right)+\left(10+12+...+98\right)\)
=(-1)+(-1)+...+(-1)
=-1x45=-45
\(b)\)\(9!-8!-7!.8^2\)
\(=\)\(8!\left(9-1\right)-7!.8^2\)
\(=\)\(7!.8.8-7!.8^2\)
\(=\)\(7!.8^2-7!.8^2\)
\(=\)\(0\)
\(c)\)\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
\(=\)\(\frac{\left(2^2\right)^2.\left(2^{16}\right)^2.3^2}{2^{13}.\left(2^2\right)^{11}.11-\left(2^4\right)^9}\)
\(=\)\(\frac{2^4.2^{32}.3^2}{2^{13}.2^{22}.11-2^{36}}\)
\(=\)\(\frac{2^{36}.3^2}{2^{35}.11-2^{36}}\)
\(=\)\(\frac{2^{36}.3^2}{2^{35}\left(11-2\right)}\)
\(=\)\(\frac{2.3^2}{9}\)
\(=\)\(\frac{2.3^2}{3^2}\)
\(=\)\(2\)
\(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)=\left(100+121+144\right):\left(169+196\right)=1\)
\(9!-8!-7!\cdot8^2=8!\left(9-1\right)-7!\cdot8^2=7!\cdot8^2-7!\cdot8^2=0\)
\(\frac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}=\frac{3^2\cdot2^{36}}{11\cdot2^{35}-2^{36}}=\frac{9\cdot2^{36}}{2^{35}\cdot\left(11-2\right)}=\frac{9\cdot2^{36}}{2^{35}\cdot9}=2\)
