Question

[Nguyễn Minh TrIết]

 M) 2¹⁹.27³+15.4⁹.9⁴

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         6⁹.2¹⁰+12¹⁰

Answer 1

[Xyz OLM]

\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}=\frac{2^{19}.3^9+3^9.2^{18}.5}{2^{19}.3^9+3^{10}.2^{20}}\)

\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{7}{2.7}=\frac{1}{2}\)

Answer 2

[Capheny Bản Quyền]

\(M=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\) 

\(=\frac{2^{19}\cdot\left(3^3\right)^3+3\cdot5\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{6^9\cdot2^{10}+6^{10}\cdot2^{10}}\) 

\(=\frac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3\cdot3^8}{6^9\cdot2^{10}\left(6+1\right)}\) 

\(=\frac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{6^9\cdot2^{10}\cdot7}\) 

\(=\frac{2^{18}\cdot3^9\left(2+5\right)}{2^{10}\cdot2^9\cdot3^9\cdot7}\) 

\(=\frac{2^{18}\cdot3^9\cdot7}{2^{19}\cdot3^9\cdot7}\) 

\(=\frac{1}{2}\)