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\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(=\frac{5.2^{30}.3^{18}-3^{20}.2^{29}}{5.2^9.3^{19}.2^{19}-7.2^{29}.3^{18}}\)
\(=\frac{5.2^{30}.3^{18}-3^{20}.2^{29}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(=\frac{3^{18}.2^{29}.\left(5+1-9+2\right)}{2^{28}.3^{18}.\left(5+3-7-2\right)}\)
\(=\frac{2.\left(-1\right)}{-1}=2\)
Vậy đáp án C đúng.
\(\frac{5.2^{30}.3^{18}-4.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(=\frac{5.2^{28}.2^2.3^{18}-4.3^{18}.3^2.2^{27}}{5.2^{28}.3^{18}.3-7.2^{27}.2^2.3^{18}}\)
\(=\frac{3^{18}.\left(5.2^{28}.4-4.9.2^{27}\right)}{3^{18}.\left(5.3.2^{28}-7.2^{27}.4\right)}\)
\(=\frac{20.2^{28}-9.2.2.2^{27}}{15.2^{28}-14.2.2^{27}}\)
\(=\frac{2^{28}.20-18.2^{28}}{15.2^{28}-14.2^{28}}\)
\(=\frac{2^{28}.\left(20-18\right)}{2^{28}.\left(15-14\right)}\)
\(=\frac{2^{28}.2}{2^{28}1}\)
\(=2\)