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= ( 2.4)10 + 411 / (2.4)4 + 48
= 210 . 410 + 411 / 24 . 44 + 48
= 26 . 421/ 2 . 412
= 27 . 49 / 2 . 4
= 26 . 48
= 26 . ( 2 . 2) 8
= 26 . 28 . 28
= 2 . 22 . 28
= 211
= 2048
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M= (2x4)^10 + 4^11 / (2x4)^4 + 4^8
M= 2^10 x 4^10 + 4^11 / 2^4 x 4^4 + 4^8
M= 2^6 x 4^21 / 2 x 4^12
M=2^7 x 4^9 / 2 x 4
M=2^6 x 4^8
M=2^6 x (2x2)^8
M=2^6 x 2^8 x 2^8 = 2 x 2^2 X 2^8 = 2^11 = 2048
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\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}.\left(2^{10}+1\right)}{2^{12}.\left(2^{10}+1\right)}=\frac{2^{20}}{2^{12}}=2^8=256\)
\(\frac{\left(8^{10}+4^{10}\right)}{\left(8^4+4^{11}\right)}\\ =\frac{\left(2^{30}+2^{20}\right)}{\left(2^{12}+2^{22}\right)}\\ =\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}\\ =\frac{2^{10}}{2^{12}}=2^2=4\)
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\(a,\dfrac{20^5.5^{10}}{100^5}=\dfrac{20^5.5^5.5^5}{100^5}=\dfrac{100^5.5^5}{100^5}=5^5\)
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\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)
\(=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\)
\(=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}\)
\(=\frac{2^{20}.\left(2^{10}+1\right)}{2^{12}.\left(2^{10}+1\right)}\)
\(=\frac{2^{20}}{2^{12}}\)
\(=2^8=256\)
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\(A=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\dfrac{2^{20}}{2^{12}}=2^8=256\)