Đề như thế này chắc đúng hơn nhỉ?
\(\frac{5.14^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
Đặt \(A=5.14^{15}.9^9-4.3^{20}.8^9\) và \(B=5.2^9.6^{19}-7.2^{29}.27^6\), ta được:
\(\text{+)}\) \(A=5.14^{15}.9^9-4.3^{20}.8^9=5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9=5.2^{30}.3^{18}-2^2.3^{20}.2^{27}\)
\(A=5.2^{30}.3^{18}-2^{29}.3^{20}=2^{29}.3^{18}\left(5.2-3^2\right)=2^{29}.3^{18}\)
\(\text{+)}\) \(B=5.2^9.6^{19}-7.2^{29}.27^6=5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6=5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}\)
\(B=5.2^{28}.3^{19}-7.2^{29}.3^{18}=2^{28}.3^{18}\left(5.3-7.2\right)=2^{28}.3^{18}\)
Do đó, \(\frac{A}{B}=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2\)
bài này nên tách ở số mũ ra rồi tính , cho nhanh
nha
