\(A=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9}{6^9\cdot2^{10}}+1^{210}\)

\(=\frac{2^{19}\cdot3^9+2^{18}\cdot3^3\cdot5}{2^9\cdot3^9\cdot2^{10}}+1\)

\(=\frac{2^{18}\cdot3^3\left(3^6+5\right)}{2^{19}\cdot3^9}+1=\frac{3^6+5}{3^6}+1=\frac{2\cdot3^6+5}{3^6}=\frac{1463}{729}\)

=\(\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)

=\(\frac{2^{19}.3^9+5.2^{18}.3.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)

\(=\frac{2^{19}.3^9+2^{18}.3^9.5}{2^{19}.3^9+2^{20}.3^{10}}\)

=\(\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}\)

\(=\frac{2^{18}.3^9.7}{2^{19}.3^9.7}=\frac{1}{2}\)

a)\(A=\frac{5.2^{13}.2^{22}-2^{36}}{\left(3.2^{17}\right)^2}\)

\(A=\frac{5.2^{35}-2^{36}}{3^2.2^{34}}\)

\(A=\frac{2^{35}\left(5-2\right)}{3^2.2^{34}}\)

\(A=\frac{2.3}{3^2}=\frac{2}{3}\)

b) \(B=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(B=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)

\(B=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(2+3\right)}\)

\(B=\frac{7}{2.5}=\frac{7}{10}\)

Câu a là 1676250 nhé

Ta có: \(1\times10+2\times9+\cdots+10\times1\)

\(=2\times\left(1\times10+2\times9+\cdots+5\times6\right)\)

\(=2\times\left(11+18+24+28+30\right)=2\times111=222\)

\(1+3+6+\cdots+45+55\)

\(=\frac{1\times2}{2}+\frac{2\times3}{2}+\frac{3\times4}{2}+\cdots+\frac{9\times10}{2}+\frac{10\times11}{2}\)

\(=\frac12\times\left(1\times2+2\times3+\cdots+10\times11\right)\)

\(=\frac12\times\left\lbrack1\times\left(1+1\right)+2\times\left(2+1\right)+\cdots+10\times\left(10+1\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\left(1\times1+2\times2+\cdots+10\times10\right)+\left(1+2+\cdots+10\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times\left(10+1\right)\times\left(2\times10+1\right)}{6}+\frac{10\times11}{2}\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times11\times21}{6}+5\times11\right\rbrack=\frac12\times\left\lbrack5\times11\times7+5\times11\right\rbrack\)

\(=\frac12\times55\times\left(7+1\right)=55\times\frac82=55\times4=220\)

Ta có: \(\frac{1+3+6+\cdots+45+55}{1\times10+2\times9+\cdots+10\times1}\)

\(=\frac{220}{222}=\frac{110}{111}\)