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Ta có : \(M=\left[\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{18}\right)+\frac{7}{8}:\left(\frac{1}{18}-\frac{4}{9}\right)\right]:\left(\frac{494949}{525252}-1\right)\)
=> \(M=\left[\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{18}+\frac{1}{18}-\frac{4}{9}\right)\right]:\left(\frac{494949}{525252}-\frac{525252}{525252}\right)\)
=> \(M=\left(\frac{7}{8}:\frac{-2}{9}\right):\left(\frac{494949}{525252}-\frac{525252}{525252}\right)\)
=> \(M=\left(-\frac{63}{16}\right):\left(-\frac{3}{52}\right)\)
=> \(M=\frac{63}{16}:\frac{3}{52}=\frac{63}{16}.\frac{52}{3}=\frac{21.3.13.4}{4.4.3}=\frac{21.13}{4}=\frac{273}{4}\)
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Câu 1 :
\(\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^5}\)
= \(\frac{5^{32}.2^{86}.5^{43}}{\left(-2\right)^{87}.5^{15}}\)
= \(\frac{5^{72}.\left(-2\right)^{86}}{\left(-2\right)^{87}.5^{75}}\)
= \(\frac{1}{-2}\)
Câu 2 :
\(\frac{5^4.18^4}{125.9^5.16}\)
= \(\frac{5^4.2^4.3^8}{5^3.3^{10}.2^4}\)
= \(\frac{5}{3^2}\)
= \(\frac{5}{9}\)
Câu 3 :
\(\frac{9^{18}.2^{29}}{8^9.27^{12}}\)
= \(\frac{3^{36}.2^{29}}{2^{27}.3^{36}}\)
= \(2^2\)
= 4
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\(\dfrac{7}{8}\): \(\left(\dfrac{2}{9}-\dfrac{1}{18}\right)\)+\(\dfrac{7}{8}\): \(\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)
= \(\dfrac{7}{8}\): \(\dfrac{1}{6}\)+\(\dfrac{7}{8}\): \(\left(\dfrac{-14}{36}\right)\)
= \(\dfrac{7}{8}\): \(\left\{\dfrac{1}{6}+\left(\dfrac{-14}{36}\right)\right\}\)
= \(\dfrac{7}{8}\): \(\left(\dfrac{-2}{9}\right)\)
= \(\dfrac{7}{8}\). \(\left(\dfrac{-9}{2}\right)\)
= \(\dfrac{-63}{16}\)
Giải:
\(\dfrac{7}{8}:\left(\dfrac{2}{9}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)
\(=\dfrac{7}{8}:\left(\dfrac{4}{18}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{15}{36}\right)\)
\(=\dfrac{7}{8}:\dfrac{3}{18}+\dfrac{7}{8}:\left(-\dfrac{7}{18}\right)\)
\(=\dfrac{7}{8}.6+\dfrac{7}{8}.\dfrac{18}{-7}\)
\(=\dfrac{7}{8}\left(6+\dfrac{18}{-7}\right)\)
\(=\dfrac{7}{8}.\dfrac{24}{7}\)
\(=3\)
Vậy giá trị của biểu thức trên là 3.
Chúc bạn học tốt!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(=\dfrac{2^{19}\cdot3^9+3^9\cdot5\cdot2^{18}}{2^{19}\cdot3^9+2^{10}}\)
\(=\dfrac{3^9\cdot2^{18}\cdot\left(2+5\right)}{2^{10}\cdot\left(2^9\cdot3^9+1\right)}=\dfrac{3^9\cdot7\cdot2^8}{6^9+1}\)
b: \(=\dfrac{\dfrac{-1}{8}-\dfrac{27}{64}\cdot4}{-2+\dfrac{9}{16}-\dfrac{3}{8}}=\dfrac{-29}{16}:\dfrac{-29}{16}=1\)
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a: \(\left(18\dfrac{1}{3}:\sqrt{225}+8\dfrac{2}{3}\cdot\sqrt{\dfrac{49}{4}}\right):\left[\left(12\dfrac{1}{3}+8\dfrac{6}{7}\right)-\dfrac{\left(\sqrt{7}\right)^2}{\left(3\sqrt{2}\right)^2}\right]:\dfrac{1704}{445}\)
\(=\left(\dfrac{55}{3}:15+\dfrac{26}{3}\cdot\dfrac{7}{4}\right):\left[\left(12+\dfrac{1}{3}+8+\dfrac{6}{7}\right)-\dfrac{7}{18}\right]\cdot\dfrac{445}{1704}\)
\(=\left(\dfrac{55}{45}+\dfrac{91}{6}\right):\left[20+\dfrac{101}{126}\right]\cdot\dfrac{445}{1704}\)
\(=\dfrac{295}{18}:\dfrac{2621}{126}\cdot\dfrac{445}{1704}\)
\(=\dfrac{295}{18}\cdot\dfrac{126}{2621}\cdot\dfrac{445}{1704}\simeq0,21\)
b: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{99\cdot100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}=\dfrac{99}{100}\)
c: \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{n+1}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{n}{n+1}\)
\(=\dfrac{1}{n+1}\)
d: \(-66\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{11}\right)+124\cdot\left(-37\right)+63\cdot\left(-124\right)\)
\(=-66\cdot\dfrac{33-22+6}{66}+124\left(-37-63\right)\)
\(=-17-12400=-12417\)
e: \(\dfrac{7}{4}\left(\dfrac{33}{12}+\dfrac{3333}{2020}+\dfrac{333333}{303030}+\dfrac{33333333}{42424242}\right)\)
\(=\dfrac{7}{4}\left(\dfrac{33}{12}+\dfrac{33}{20}+\dfrac{33}{30}+\dfrac{33}{42}\right)\)
\(=\dfrac{7}{4}\cdot33\cdot\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)\)
\(=33\cdot\dfrac{7}{4}\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(=33\cdot\dfrac{7}{4}\cdot\left(\dfrac{1}{3}-\dfrac{1}{7}\right)\)
\(=33\cdot\dfrac{7}{4}\cdot\dfrac{4}{21}=\dfrac{33\cdot1}{3}=11\)
\(9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\)
= \(18^8-18^2+1=1\)
\(9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\)
\(=18^8-\left(18^8-1\right)\)
\(=18^8-18^8+1\)
\(=1\)