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4 6 . 9 5 + 6 9 . 120 8 4 . 3 12 − 6 11 = 2 2 6 . 3 2 5 + 2 9 .3 9 .2 3 .3.5 2 3 4 .3 12 − 2 11 .3 11 = 2 12 .3 10 + 2 12 .3 10 .5 2 12 .3 12 − 2 11 .3 11 = 2 12 .3 10 1 + 5 2 11 .3 11 2.3 − 1 = 2.6 3.5 = 4 5
`#3107.101107`
\(\dfrac{4^{10}\cdot9^6+3^{12}\cdot8^5}{6^{13}\cdot4-2^{16}\cdot3^{12}}\)
\(=\dfrac{2^{20}\cdot3^{12}+3^{12}\cdot2^{15}}{2^{13}\cdot3^{13}\cdot2^2-2^{16}\cdot3^{12}}\)
\(=\dfrac{3^{12}\cdot\left(2^{20}+2^{15}\right)}{3^{12}\cdot\left(2^{15}\cdot3-2^{16}\right)}\)
\(=\dfrac{2^{20}+2^{15}}{2^{15}\cdot3-2^{16}}\)
\(=\dfrac{2^{15}\cdot\left(2^5+1\right)}{2^{15}\cdot\left(3-2\right)}\)
\(=\dfrac{32+1}{1}\)
\(=33\)