\(\frac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{2^{12}\cdot3^{24}\cdot5^{12}\cdot2^9\cdot3^3}=\frac{3\cdot3^{27}\cdot5^{10}\cdot2^{21}}{2^{21}\cdot3^{27}\cdot5^2\cdot5^{10}}=\frac{3}{5^2}=\frac{3}{25}\)

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

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

\(=\)\(\frac{3.3^{27}.5^{10}.2^{21}}{2^{21}.3^{27}.5^2.5^{10}}\)

\(=\)\(\frac{3}{5^2}\)

\(=\)\(\frac{3}{25}\)

Ta có: \(\dfrac{9^{14}\cdot225^2\cdot8^7}{18^{12}\cdot625^3\cdot24^3}\)

\(=\dfrac{3^{32}\cdot5^4\cdot2^{21}}{2^{12}\cdot3^{14}\cdot5^{12}\cdot2^9\cdot3^3}\)

\(=\dfrac{3^{15}}{5^8}\)

\(\dfrac{9^{14}.225^2.8^7}{18^{12}.625^3.24^3}=\dfrac{3^{28}.3^2.5^2.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3^3}=\dfrac{3^3}{5^{10}}\)

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}=\frac{3}{5^2}=\frac{3}{25}\)

\(\frac{9^{14}.25^5.8^2.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^{10}.8^9}{2^{12}.9^{12}.5^{12}.3^3.2^9}\)\(=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{24}.3^3}=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{27}}\)  \(=\frac{3.2^6}{5^2}=\frac{192}{25}=7,68\)

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\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}\)

\(=3.5^{-2}\)

đổi ra thành thừa số nguyên tố rồi (ví dụ 9^2=(3^2)^2=3^4) rồi rút gọn là ra!!!

\(\frac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{9^{14}\cdot25^5\cdot8^7}{9^{12}\cdot2^{12}\cdot25^6\cdot8^3\cdot3^3}=\frac{9^2\cdot8^4}{2^{12}\cdot25\cdot3^3}=\frac{3}{25}\)

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{9^{14}.25^5.8^7}{9^{12}.2^{12}.25^6.8^3.3^3}=\frac{9^{12}.9.9.25^5.8^3.8.8.8.8}{9^{12}.2^{12}.25^5.25^1.8^3.3^3}=\frac{9.9.8.8.8.8}{2^{12}.25.3^3}\)

\(\Leftrightarrow\frac{9^2.8^4}{2^{12}.25.3^3}=\frac{3}{25}\)