\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}.\left(2^{10}+1\right)}{2^{12}.\left(1+2^{10}\right)}=\frac{2^8}{1}=256\)
\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\\ =\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\\ =\frac{2^{30}+2^{20}}{2^{12}+2^{22}}\\ =\frac{4^{15}+4^{10}}{4^6+4^{11}}\\ =\frac{4^{10}\left(4^5+1\right)}{4^6\left(1+4^5\right)}\\ =\frac{4^{10}}{4^6}\\ =4^4\\ =256\)
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\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{32}}=\frac{2^{20}.\left(2^{10}+1\right)}{2^{12}.\left(1+2^{10}\right)}=\frac{2^8}{1}=256\)
M=84+411810+410=(23)4+(22)11(23)10+(22)10
=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=212+222230+220=212(210+1)220(210+1)
=\frac{2^{10}}{2^{12}}=\frac{1}{2^2}=\frac{1}{4}=212210=221=41