Rut gon roi tinh: ( \(\frac{12^2}{4^2.6^2}\) - \(\frac{15^3}{25^2.6^2}\) - \(\frac{8^2.9^2}{4^3.6^4}\) )
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Ta có:
\(\frac{5^2.6^{11}.16^2.6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\) = \(\frac{5^2.6^{11}.6^2.6^2.6^6.2^6.3^2.5^2}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{15}.3^3}\) = \(\frac{5^6.6^{21}.2^8.3^2}{2^{17}.3^{12}.5^4-3^{11}.2^{15}}\) = \(\frac{5^6.3^{23}.2^{29}}{3^{11}.2^{15}.\left(2^2.3.5^4-1\right)}\)
= \(\frac{5^6.3^{13}.2^{14}}{2^2.3.5^4-1}\)
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Ta có
\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\cdot\frac{5^4.20^4}{25^5.4^5}\)
\(=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\cdot\frac{2^8.5^8}{5^{10}.2^{10}}\)
\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}\cdot\frac{1}{5^2.2^2}\)
\(=\frac{\left(-2\right)}{6}\cdot\frac{1}{100}=-\frac{1}{3}\cdot\frac{1}{100}=-\frac{1}{300}\)
Vậy : \(E=-\frac{1}{300}\)
Bài làm
\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}.\frac{5^4.20^4}{25^5.4^5}\)
\(\Rightarrow E=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}.\frac{5^4.4^4.5^4}{5^{10}.4^5}\)
\(\Rightarrow E=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}.\frac{5^8.4^4}{5^{10}.4^5}\)
\(\Rightarrow E=\frac{2^{10}\left(3^8-3^9\right)}{2^{10}\left(3^8+3^8.5\right)}.\frac{1}{5^2.4}\)
\(\Rightarrow E=\frac{3^8-3^9}{3^8\left(1+5\right)}.\frac{1}{100}\)
\(\Rightarrow E=\frac{3^8\left(1-3\right)}{3^8\left(1+5\right)}.\frac{1}{100}\)
\(\Rightarrow E=-\frac{2}{6}.\frac{1}{100}\)
\(\Rightarrow E=-\frac{1}{300}\)