Tính A
A=\(\dfrac{3^6\cdot45^4-15^{13}\cdot\left(\dfrac{1}{5}\right)^9}{27^4\cdot25^3+45^6}\)
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13 tháng 9 2021
\(a,=\dfrac{3^6\cdot5^4\cdot9^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+9^6\cdot5^6}=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}\\ =\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
13 tháng 9 2021
\(b,=\dfrac{\left(\dfrac{2}{5}\cdot5\right)^7+\left(\dfrac{9}{4}\cdot\dfrac{16}{3}\right)^3}{2^7\cdot5^2+2^9}=\dfrac{2^7+12^3}{2^7\left(5^2+2^2\right)}=\dfrac{2^7+4^3\cdot3^3}{2^7\cdot29}=\dfrac{2^6\left(2+3^3\right)}{2^7\cdot29}=\dfrac{1}{2}\)
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\(A=\dfrac{3^6.45^4-15^{13}.\left(\dfrac{1}{5}\right)^9}{27^4.25^3+45^6}\)
\(=\dfrac{3^6.3^8.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{13}\left[3.5^4-5^{13}.\left(\dfrac{1}{5}\right)^9\right]}{3^{12}(5^6+5^6)}\)
\(=\dfrac{3^{13}.1250}{3^{12}.31250}\)
\(=\dfrac{3^{13}.5^4.2}{3^{12}.5^6.2}\)
\(=\dfrac{3}{5^2}=\dfrac{3}{25}\)
Vậy \(A=\dfrac{3}{25}\)