Bài 1: Rút gọn

\(A=\dfrac{-56\cdot49+\left(-49\right)\cdot44}{73\cdot14+\left(-14\right)\cdot\left(-27\right)}\)

\(=\dfrac{49\cdot\left(-56-44\right)}{14\cdot\left(73+27\right)}\)

\(=\dfrac{-49\cdot100}{14\cdot100}=\dfrac{-7}{2}\)

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{25}.5^{12}}\)

\(=\frac{3^3.1.1}{1.1.5^2}\)

\(=\frac{27}{25}\)

Sai rồi

\(\frac{15.8+15.4}{12.3}=\frac{15.\left(8+4\right)}{12.3}=\frac{15.12}{12.3}=\frac{5}{1}=5\)

\(\frac{15.8+15.4}{12.3}=\frac{15.\left(8+4\right)}{12.3}=\frac{5.12}{4.3}=\frac{5}{1}=5\)

\(\frac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{\left(3^2\right)^{14}\cdot\left(5^2\right)^5\cdot\left(2^3\right)^7}{\left(3^2\cdot2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(3\cdot2^3\right)^3}\)

\(=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{24}\cdot2^{12}\cdot5^{12}\cdot3^3\cdot2^9}=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{25}\cdot5^{12}\cdot2^{21}}=\frac{3^3}{5^2}=\frac{27}{25}\)

\(\frac{9^{14}}{18^{12}}.\frac{25^5}{625^3}.\frac{8^7}{24^3}\)

\(=\frac{9^{14}}{\left(9.2\right)^{12}}.\frac{25^5}{25^6}.\frac{8^7}{\left(8.3\right)^3}\)

\(=\frac{9^{14}}{9^{12}.2^{12}}.\frac{1}{25}.\frac{8^7}{8^3.3^3}\)

\(=\frac{9^2}{2^{12}}.\frac{1}{25}.\frac{8^4}{3^3}\)

\(=\frac{81}{4096}.\frac{1}{25}.\frac{4096}{27}\)

\(=\frac{81}{4096}.\frac{4096}{27}.\frac{1}{24}=3.\frac{1}{24}=\frac{3}{24}\)

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Ngu voi ko biet lam

\(\frac{9^{14}.225^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(3^2.5^2\right)^5.\left(2^3\right)^7}{\left(3^2.2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}=\frac{3^{28}.3^{10}.5^{10}.2^{21}}{3^{24}.2^{12}.5^{12}.3^3.2^9}=\frac{3^{38}.5^{10}.2^{21}}{3^{27}.2^{21}.5^{12}}=\frac{3^{11}}{5^2}\)