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\(\frac{4^5.9^5-2.6^{10}}{2^{10}.3^9+6^9.20}=\frac{\left(4.9\right)^5-2.2^{10.}.3^{10}}{2^{10}.3^9+2^9.3^9.2^2.5}\)
\(\frac{2^{10}.3^{10}^{ }-2^{11}.3^{10}}{2^{10}.3^9+2^{11}.3^9.5}=\frac{2^{10}.3^{10}\left(1-2\right)}{2^{10}.3^9\left(1+2.5\right)}\)
\(\frac{2^{10}.3^{10}.\left(-1\right)}{2^{10}.3^9.\left(-9\right)}=\frac{-3}{-9}=\frac{1}{3}\)
Có: \(5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9=5\cdot2^{30}\cdot3^{18}-2^2\cdot3^{20}\cdot2^{27}=5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{29}\)
\(=3^{18}\cdot2^{29}\cdot\left(5\cdot2-3^2\right)=3^{18}\cdot2^{29}\)
Lại có: \(5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6=5\cdot2^{10}\cdot2^{19}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}=5\cdot2^{29}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}\)
\(=2^{19}\cdot3^{18}\cdot\left(5\cdot3-7\right)=2^{19}\cdot3^{18}\cdot2^3=2^{22}\cdot3^{18}\)
Vậy \(\frac{3^{18}\cdot2^{29}}{2^{22}\cdot3^{18}}=2^7=128\)
\(A=\frac{2^{19}.\left(2^3\right)^3+15.\left(2^2\right)^9.\left(3^2\right)^4}{2^9.3^9.2^{10}+\left(2^2.3\right)^{10}}=\frac{2^{19}.3^9+15.2^{18}.3^8}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^8.\left(2.3+15\right)}{2^{19}.3^9.\left(1+2.3\right)}\)
\(=\frac{2^{18}.3^8.21}{2^{19}.3^9.7}=\frac{21}{2.3.7}=\frac{1}{2}\)
\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)
\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)
\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)
\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)
\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)
\(=0,2-\dfrac{2}{3}\)
\(=-\dfrac{7}{15}\)
\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)
\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)
\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)
\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)
\(=\dfrac{13}{26}\)
\(=\dfrac{1}{2}\)
#\(Toru\)
\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)
ai làm nhanh , trình bày rõ ràng 10 tk
\(\frac{\frac{6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}=\frac{6\left(\frac{1}{5}+\frac{1}{19}-\frac{1}{23}\right)}{9\left(\frac{1}{5}-\frac{1}{19}+\frac{1}{23}\right)}=\frac{6}{9}=\frac{2}{3}\)