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\(\frac{35\left(27^8+2.9^{11}\right)}{15\left(81^6-12.3^{19}\right)}\)= \(\frac{35\left(\left(3^3\right)^8+2.\left(3^2\right)^{11}\right)}{15\left(\left(3^4\right)^6-4.3.3^{19}\right)}\)= \(\frac{35\left(3^{24}+2.3^{22}\right)}{15\left(3^{24}-4.3^{20}\right)}\)= \(\frac{35\left(3^{22}.3^2+2.3^{22}\right)}{15\left(3^{20}.3^4-4.3^{20}\right)}\)= \(\frac{35\left(3^{22}.\left(9+2\right)\right)}{15\left(3^{20}.\left(81-4\right)\right)}\)= \(\frac{35\left(3^{22}.11\right)}{15\left(3^{20}.77\right)}\)= \(\frac{5.7.3^{22}.11}{5.3.3^{20}.7.11}\)= \(\frac{3^{22}}{3.3^{20}}\)= \(\frac{3^{20}.3.3}{3.3^{20}}\)= \(\frac{3}{1}\)= 3
\(\frac{35.\left(27^8+2.9^{11}\right)}{15\left(81^6-12.3^{19}\right)}=\frac{5.7\left(3^{24}+2\cdot3^{22}\right)}{3.5\left(3^{24}-2^2.3^{20}\right)}\)
Câu 3:
a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)
\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)
b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)
\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)
Câu 4:
a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)
b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)
\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)
\(=-27\cdot100-23\cdot100\)
\(=100\left(-27-23\right)\)
\(=-50\cdot100=-5000\)
c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)
d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)
\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)
\(=-1+1+\dfrac{5}{6}\)
\(=\dfrac{5}{6}\)
\(\frac{35\left(27^8+2.9\right)}{15\left(8^{16}-12.3^{19}\right)}\)
\(=\frac{7.\left(3^{24}+2.3^2\right)}{2^{48}-2^2.3^{20}}\)
\(=\frac{3^2.7.\left(3^{20}+2\right)}{2^2.\left(2^{46}-3^{20}\right)}\)