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\(\frac{3^6.45^4-15^{13}.9^{-9}}{27^4.25^3+45^6}=\frac{3^6.\left(3.3.5\right)^4-\left(3.5\right)^{13}-\left(3^2\right)^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3.15\right)^6}=\frac{3^6.3^4.3^4.5^4-3^{13}.5^{13}-3^{-18}}{3^{12}.5^6+3^6.15^6}=\frac{3^{14}.5^4-3^{13}.5^{13}-3^{-18}}{3^{12}.5^6+3^6.\left(3.5\right)^6}=\frac{ }{ }\)
Mình nghĩ hết được rồi
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{3^6.45^4-15^{13}.\left(\dfrac{1}{5}\right)^9}{27^4.25^3+45^6}\)
\(=\dfrac{3^6.3^8.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{13}\left[3.5^4-5^{13}.\left(\dfrac{1}{5}\right)^9\right]}{3^{12}(5^6+5^6)}\)
\(=\dfrac{3^{13}.1250}{3^{12}.31250}\)
\(=\dfrac{3^{13}.5^4.2}{3^{12}.5^6.2}\)
\(=\dfrac{3}{5^2}=\dfrac{3}{25}\)
Vậy \(A=\dfrac{3}{25}\)