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\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}=\frac{3}{5^2}=\frac{3}{25}\)
\(\frac{374}{506}=\frac{2.187}{253.2}=\frac{187}{253}\)
\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.9^{12}.5^{12}.3^3.8^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}\)
\(=\frac{3}{5^2}\)
\(\frac{9^{14}.25^5.8^2.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^{10}.8^9}{2^{12}.9^{12}.5^{12}.3^3.2^9}\)\(=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{24}.3^3}=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{27}}\) \(=\frac{3.2^6}{5^2}=\frac{192}{25}=7,68\)
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