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\(5.4^{15}.9^9-4.3^{20}.8^9\)
\(=5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9\)
\(=5.2^{30}.3^{18}-2^2.3^{20}.2^{27}\)
\(=5.2^{29}.3.3^{18}-3^{18}.3^2.2^{29}\)
\(=3^{18}.2^{29}.\left(15-9\right)\)
\(=3^{18}.2^{29}.6\)
\(=3^{18}.2^{29}.2.3\)
\(=3^{19}.2^{30}\)
\(5.2^6.6^{19}-7.2^{29}.27^6\)
\(=5.2^6.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6\)
\(=5.2^6.2^{19}.3^{19}-7.2^{29}.3^{18}\)
\(=5.2^{25}.3^{18}.3-7.2^{25}.2^4.3^{18}\)
\(=2^{25}.3^{18}.\left(15-112\right)\)
\(=2^{25}.3^{18}.\left(-97\right)\)
5.415.99-4.320.89=5.230.318-229.320=229.318.(5.2-32)=229.318
5.29.619-7.229.276=5.228.319-7.229.318=228.318.(5.3-7.2)=228.318
Đề bài sai ak bn :
\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}\)
\(=\frac{5.2^{30}.3^{18}-3^{20}.2^{29}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}=\frac{2^{29}.3^{18}.1}{2^{28}.3^{18}.1}=\frac{2^{29}}{2^{28}}=2\)