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\(\frac{\left(-0,25\right)^{-5}.9^4.\left(-2\right)^{-3}-2^{-2}.6^9}{2^9.3^6+6^6.40}\)
\(=\frac{\left(-4\right)^5.\left(3^2\right)^4.\left(-2\right)^{-3}-2^{-2}.\left(3.2\right)^9}{2^9.3^6+\left(2.3\right)^6.2^3.5}\)
\(=\frac{-\left(2^2\right)^5.3^8.\left(-2\right)^{-3}-2^{-2}.3^9.2^9}{2^9.3^6+2^6.3^6.2^3.5}\)
\(=\frac{-2^{10}3^8.\left(-2\right)^{-3}-2^7.3^9}{2^9.3^6+2^9.3^6.5}\)
\(=\frac{2^73^8.-2^7.3^9}{2^9.3^6+2^9.3^6.5}\)
\(=\frac{2^7.3^8.\left(1-3\right)}{2^9.3^6.\left(1+5\right)}\)
\(=\frac{3^2.\left(-2\right)}{2^2.6}\)
\(=\frac{-3}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm :
\(\frac{4^6\times9^5+120\times6^9}{8^4\times3^{12}-6^{11}}\)
\(=\frac{\left(2^2\right)^6\times\left(3^2\right)^5+2^3\times5\times3\times\left(2\times3\right)^9}{\left(2^3\right)^4\times3^{12}-\left(2\times3\right)^{11}}\)
\(=\frac{2^{12}\times3^{10}+2^3\times5\times3\times2^9\times3^9}{2^{12}\times3^{12}-2^{11}\times3^{11}}\)
\(=\frac{2^{12}\times3^{10}\times\left(1+5\right)}{2^{11}\times3^{11}\times\left(2\times3-1\right)}\)
\(=\frac{2\times6}{3\times5}\)
\(=\frac{4}{5}\)
Học tốt nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
:V Làm sai hết rồi sai ngay từ bước đầu tiên.
\(\frac{1}{3.4}-\frac{1}{4.5}-\frac{1}{5.6}-....-\frac{1}{9.10}\)
\(=\frac{1}{3.4}-\left(\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{9.10}\right)\)
\(=\frac{1}{12}-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{12}-\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(=\frac{1}{12}-\frac{3}{20}\)
\(=\frac{-11}{12}\)
\(\frac{1}{3.4}-\frac{1}{4.5}-...-\frac{1}{9.10}\)
= \(-\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
= \(-\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
= \(-\left(\frac{1}{3}-\frac{1}{10}\right)\)
= \(-\frac{7}{30}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
1/2x6 + 1/4x9 + 1/6x12 +...+1/198 x 300
= 1/6x2 + 1/6x6 + 1/6x12 + ....+1/6x9900
= 1/6 x ( 1/2 + 1/6 + 1/ 12 +...+1/9900)
= 1/6 x (1/1x2 + 1/2x3 + 1/3x4+...+1/99x100)
=1/6x (1-1/2 + 1/2-1/3 + 1/3 - 1/4 + ....+1/99-1/100)
=1/6x(1-1/100)
=1/6 x 99/100
= 33/200
k cho mình nha , học tốt