Question

rút gọn phân số

\(\frac{2^{19}.27^3+15.4^4.9^4}{6^9.2^{10}+12^{10}}\)

Answer 1

\(\frac{2^{19}.27^3+15.4^4.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.3^9+5.2^8.3^9}{2^9.3^9+2^{20}.3^{10}}=\frac{2^8.3^9\left(2^{11}-5\right)}{2^9.3^9\left(1+2^{11}.3\right)}=\frac{2043}{2.6145}=\frac{2043}{12290}\)

Answer 2

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

\(=\frac{2^{19}\cdot3^9+3\cdot5\cdot2^8\cdot3^8}{2^9\cdot3^9+2^{20}\cdot3^{10}}\)

\(=\frac{2^8\cdot3^9\left(2^{11}+5\right)}{2^9\cdot3^9\left(2^{11}\cdot3+1\right)}\)

\(=\frac{\left(2^{11}+5\right)}{2\left(2^{11}\cdot3+1\right)}\)

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