\(\frac{27^3+9^{10}.2^4+4^2.81^5}{3^{10}+3^{21}.2^5}\)
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a) \(k=\frac{2^{11}.9^2}{3^5.16^2}=\frac{2^{11}.\left(3^2\right)^2}{3^5.\left(2^4\right)^2}=\frac{2^{11}.3^4}{3^5.2^8}=\frac{8.1}{3.1}=\frac{8}{3}\)
b) \(N=\frac{9^3.27^2}{6^2.3^{10}}=\frac{\left(3^2\right)^3.\left(3^3\right)^2}{\left(2.3\right)^2.3^{10}}=\frac{3^6.3^6}{2^2.3^2.3^{10}}=\frac{3^{12}}{4.3^{12}}=\frac{1}{4}\)
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b) \(\frac{4}{10}+\frac{-2}{9}+\frac{-3}{-5}+\frac{21}{-27}+\frac{-10}{20}\)
\(=\frac{2}{5}-\frac{2}{9}+\frac{3}{5}-\frac{7}{9}-\frac{1}{2}\)
\(=\left(\frac{2}{5}+\frac{3}{5}\right)-\left(\frac{2}{9}+\frac{7}{9}\right)-\frac{1}{2}\)
\(=1-1-\frac{1}{2}=-\frac{1}{2}\)
a) \(-\frac{5}{2}+\frac{1}{7}+\frac{6}{7}+\frac{1}{2}+\frac{3}{4}\)
\(=\left(\frac{-5}{2}+\frac{1}{2}\right)+\left(\frac{1}{7}+\frac{6}{7}\right)+\frac{3}{4}\)
\(=-2+1+\frac{3}{4}\)
\(=-1+\frac{3}{4}\)
\(=-\frac{1}{4}\)
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a) \(K=\frac{2^{11}\cdot9^2}{3^5\cdot16^2}=\frac{2^{11}\cdot3^4}{3^5\cdot2^8}=\frac{2^3}{3}=\frac{8}{3}\)
b) \(N=\frac{9^3\cdot27^2}{6^2\cdot3^{10}}=\frac{3^6\cdot3^6}{2^2\cdot3^2\cdot3^{10}}=\frac{1}{4}\)
c) \(P=\frac{27^{15}\cdot5^3\cdot8^4}{25^2\cdot81^{11}\cdot2^{11}}=\frac{3^{45}\cdot5^3\cdot2^{12}}{5^4\cdot3^{44}\cdot2^{11}}=\frac{3\cdot2}{5}=\frac{6}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{27^3+9^{10}.2^4+4^2.81^5}{3^{10}+3^{21}.2^5}\)
=\(\frac{3^9+3^{20}.2^4+2^4.3^{20}}{3^{10}+3^{21}.2^5}\)
=\(\frac{3^{18}+2^3}{1}\)
= \(3^{18}+2^3\)
Hk tốt