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a) \(\frac{81}{16}\)
b) \(\frac{-31}{8}\)
c) \(\frac{2417}{2401}\)
Bn làm đầy đủ ra giúp mik với !! Thầy mik bắt làm đầy đủ cơ !!!
\(4\cdot\left(\frac{1}{4}\right)^2+25\cdot\left[\left(\frac{3}{4}\right)^3\div\left(\frac{5}{4}\right)^3\right]\div\left(\frac{3}{2}\right)^3\)
\(=4\cdot\frac{1}{16}+25\cdot\left[\left(\frac{3}{4}\div\frac{5}{4}\right)^3\right]\div\left(\frac{3}{2}\right)^3\)
\(=\frac{1}{4}+25\cdot\left(\frac{3}{5}\right)^3\div\left(\frac{3}{2}\right)^3\)
\(=\frac{1}{4}+25\cdot\left(\frac{2}{5}\right)^3\)
\(=\frac{1}{4}+25\cdot\frac{8}{125}\)
\(=\frac{1}{4}\cdot\frac{8}{5}\)
\(=\frac{2}{5}\)
\(4.\left(\frac{1}{4}\right)^2+25.\left[\left(\frac{3}{4}\right)^3:\left(\frac{5}{4}\right)^3\right]:\left(\frac{3}{2}\right)^3\)
\(=4.\frac{1}{16}+25\left[\left(\frac{3}{4}:\frac{5}{4}\right)^3:\right]:\left(\frac{3}{2}\right)^3\)
\(=\frac{1}{4}+25.\left(\frac{3}{5}\right)^3:\left(\frac{3}{2}\right)^3\)
\(=\frac{1}{4}+25.\left(\frac{2}{5}\right)^3\)
\(=\frac{1}{4}+25.\frac{8}{125}\)
\(=\frac{1}{4}+\frac{8}{5}\)
\(=\frac{2}{5}\)
a)\(\left(\frac{5}{2}-\frac{4}{3}\right).\frac{6}{7}+\left(-\frac{3}{2}\right)^5:\left(-\frac{3}{2}\right)^3=\left(\frac{15}{6}-\frac{8}{6}\right).\frac{6}{7}+\left(-\frac{3}{2}\right)^2=\frac{7}{6}.\frac{6}{7}+\frac{9}{4}=\frac{9}{4}\)
\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)
\(=3-\left(-1\right)\)
\(=4\)
b) \(=\left(\frac{1}{4}+\frac{25}{2}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right)\)
\(=\left(\frac{4}{16}+\frac{200}{16}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3.3}{2.3.4}-\frac{2}{2.3.4}\right)\right)\)
\(=\left(\frac{199}{16}\right):\left(12-\frac{7}{12}:\left(\frac{9}{24}-\frac{2}{24}\right)\right)\)
\(=\frac{199}{16}:\left(12-\frac{7}{12}.\frac{24}{7}\right)\)
\(=\frac{199}{16}:\left(12-2\right)\)
\(=\frac{199}{16}:10\)
\(=\frac{199}{160}\)
c) \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)
\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)
\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)
\(=1+\frac{1}{2}\cdot\frac{\left(1+2\right)\cdot2}{2}+\frac{1}{3}\cdot\frac{\left(1+3\right)\cdot3}{2}+...+\frac{1}{20}\cdot\frac{\left(1+20\right)\cdot20}{2}\)
\(=1+\frac{1\cdot\left(1+2\right)\cdot2}{2\cdot2}+\frac{1\cdot\left(1+3\right)\cdot3}{3\cdot2}+...+\frac{1\cdot\left(1+20\right)\cdot20}{20\cdot2}\)
\(=1+\frac{1+2}{2}+\frac{1+3}{2}+...+\frac{1+20}{2}\)
\(=1+\frac{1+2+1+3+...+1+20}{2}\)
\(=1+\frac{\left(1+1+...+1\right)+\left(2+3+...+20\right)}{2}\)
\(=1+\frac{19+\left(20+2\right)\cdot19:2}{2}\)
\(=1+\frac{19+209}{2}\)
\(=1+114=115\)
a) \(\frac{\left(-1\right)}{4}^2+\frac{3}{8}.\left(\frac{-1}{6}\right)-\frac{3}{16}:\left(\frac{-1}{2}\right)=\left(\frac{-1}{4}\right)^2+\left(\frac{-3}{68}\right)-\left(\frac{-3}{8}\right)=\left(\frac{1}{16}\right)+\left(\frac{-3}{68}\right)-\left(\frac{-3}{8}\right)=\frac{5}{272}-\left(\frac{-3}{8}\right)=\frac{107}{272}\)
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
Giải :
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
~~Học tốt~~
\(2^3+3\cdot\left(\frac{1}{2}\right)^0-1+\left[\left(-2\right)^2:\frac{1}{2}\right]-8\)
\(=8+3\cdot1-1+\left[4:\frac{1}{2}\right]-8\)
\(=8+3-1+\left[4\cdot\frac{2}{1}\right]-8\)
\(=8+3-1+8-8\)
\(=11-1+0\)
\(=10\)
mọi ng giup mk đi