a: \(A=27\cdot36+27\cdot14+73\cdot99-49\cdot73\)
\(=27\cdot50+73\cdot50=50\cdot100=5000\)
b: \(B=21\cdot721+21\cdot29+79\cdot271+79\cdot29\)
\(=721\left(21+79\right)+29\left(21+79\right)\)
\(=750\cdot100=75000\)
c: \(C=\dfrac{2^{10}\cdot2\cdot5\cdot5^6+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}\)
\(=\dfrac{2^{11}\cdot5^7+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}\)
\(=\dfrac{2^8\cdot5^7\left(2^3+5^3\right)}{2^5\cdot5^4\left(2^3+5^3\right)}=2^3\cdot5^3=1000\)
d:
\(D=\dfrac{100+121+144}{169+196}=\dfrac{365}{365}=1\)
e: \(E=\dfrac{3^2\cdot2^{36}}{11\cdot2^{13}\cdot2^{22}-2^{36}}\)
\(=\dfrac{9\cdot2^{36}}{11\cdot2^{35}-2^{36}}=\dfrac{9\cdot2^{36}}{2^{35}\left(11-2\right)}=2\)
