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\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\dfrac{3^6.3^85^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\dfrac{3^{13}.5^4\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}=\dfrac{3}{25}\)
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\(\frac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)=\(\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}\)=\(\frac{3}{25}\)
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\(\frac{3^6.3^6.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{12}.5^4-3^{13}.5^7}{2.3^{12}.5^6}\) \(=\frac{3^{12}.5^4.\left(1-5^3\right)}{3^{12}.5^6.2}=\frac{-124}{5^2.2}=\frac{-62}{25}\) =2,48
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Ta có : \(A=\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3.45^6}\)
=\(\frac{3^6.5^4.3^8-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+5^6.3^{12}}\)
=\(\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+5^6.3^{12}}=\frac{3^{13}.5^4.\left(3-1\right)}{5^6.3^{12}.\left(1+1\right)}=\frac{3}{5^2}=\frac{3}{25}\)
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\(\frac{3^6.3^8.5^4-3^{13}.5^{13}:5^9}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\frac{2.3^{13}.5^4}{2.3^{12}.5^6}=\frac{1}{75}\)