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\(\frac{2^{10}\cdot13+2^{10}\cdot37}{2^8\cdot90}\)
\(=\frac{2^{10}\cdot\left(13+37\right)}{2^8\cdot2\cdot3^2\cdot5}\)
\(=\frac{2^{10}\cdot50}{2^9\cdot3^2\cdot5}\)
\(=\frac{2^{10}\cdot2\cdot5^2}{2^9\cdot3^2\cdot5}=\frac{2^{11}\cdot5^2}{2^9\cdot3^2\cdot5}\)
\(=\frac{2^2\cdot5}{3^2}=\frac{20}{9}\)
\(\frac{2^{10}.13+2^{10}.27}{2^8.90}\)
=\(\frac{2^{10}.\left(13+27\right)}{2^8.90}\)
=\(\frac{2^{10}.40}{2^8.90}\)
=\(\frac{2^2.4}{1.9}\)
=\(\frac{4.4}{9}\)
=\(\frac{16}{9}\)
\(A=2.3+3.4+4.5+...+49.50\)
\(3A=2.3.3+3.4.3+4.5.3+...+49.50.3\)
\(3A=2.3.\left(4-1\right)+3.4.\left(5-2\right)+4.5.\left(6-3\right)+...+49.50.\left(51-48\right)\)
\(3A=2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+49.50.51-48.49.50\)
\(3A=-1.2.3+49.50.51\)
\(3A=-6+48450\)
\(3A=48444\)
\(A=\frac{48444}{3}\)
\(A=16148\)
Chúc bạn học tốt ~
\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{25.26.27}\)
\(2B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{25.26.27}\)
\(2B=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{25.26}-\frac{1}{26.27}\)
\(2B=\frac{1}{1.2}-\frac{1}{26.27}\)
\(2B=\frac{1}{2}-\frac{1}{702}\)
\(2B=\frac{175}{351}\)
\(B=\frac{175}{251}:2\)
\(B=\frac{175}{502}\)
Chúc bạn học tốt ~
\(A=\frac{15.3^{11}+4.27^1}{9^7}\)
\(\Rightarrow A=\frac{3.5.3^{11}+4.3^{3^1}}{\left(3^2\right)^7}\)
\(\Rightarrow A=\frac{3^{12}.5+4.3^3}{3^{14}}\)
\(\Rightarrow A=\frac{3^3.\left(5.3^8+4.3^3\right)}{3^{14}}\)
\(\Rightarrow A=\frac{32805+4}{177147}\)
\(\Rightarrow A=\frac{32809}{177147}\)
\(\frac{2^{10}\cdot55+2^{10}\cdot26}{2^8\cdot27}\)
\(=\frac{2^{10}\left(55+26\right)}{2^8\cdot27}\)
\(=\frac{2^{10}\cdot\text{81}}{27}\)
\(=2^2\cdot3\)
\(=12\)
\(\frac{2^{10}.55+2^{10}.26}{2^8.27}=\frac{2^{10}.\left(55+26\right)}{2^8.27}\)
\(=\frac{2^2.81}{27}\)
\(=2^2.3\)
\(=12\)