D=4^19+8^7:256^4+32^3
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\(4^{19}=2^{2.19}=2^{38}\)
\(8^7=2^{3.7}=2^{21}\)
\(256^4=2^{8.4}=2^{32}\)
\(32^3=2^{5.3}=2^{15}\)
\(\Rightarrow E=\frac{2^{38}+2^{21}}{2^{32}+2^{15}}=\frac{2^{21}.\left(2^{17}+1\right)}{2^{15}.\left(2^{17}+1\right)}=\frac{2^{21}}{2^{15}}=2^6=64\)
\(\frac{4^{19}+8^7}{256^4+32^2}=\frac{\left(2^2\right)^{19}+\left(2^3\right)^7}{\left(2^8\right)^4+\left(2^5\right)^2}=\frac{2^{38}+2^{21}}{2^{32}+2^{10}}=\frac{2^{21}.\left(2^{17}+1\right)}{2^{10}.\left(2^{22}+1\right)}=\frac{2^{11}.\left(2^{17}+1\right)}{2^{22}+1}=\frac{2^{28}+2^{11}}{2^{22}+1}\)
Đặt A=7/2+7/4+...+7/256
=>2A=7+7/2+...+7/128
=>A=7-7/256=7*255/256=1785/256
1/ 2 + 2 = 4
2/ 4 + 4 = 8
3/ 8 + 8 = 16
4/ 16 + 16 = 32
5/ 32 + 32 =64
6/ 64 + 64 =128
7/ 128 + 128 =256
8/ 256 + 256 =512
9/ 521 + 512 =1033
10/ 2048 + 2048 =4096
\(D=4^{19}+8^7\div256^4+32^3=\left(2^2\right)^{19}+\left(2^3\right)^7\div\left(2^8\right)^4+\left(2^5\right)^3=2^{38}+2^{21}\div2^{32}+2^{15}=2^{15}\times\left(2^{23}+1\right)+2^{-11}\)
\(D=2^{38}+2^{21}:2^{32}+2^{15}=2^{38}+2^{^{-11}}+2^{15}\)