a) Ta có \(A=\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\dfrac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.2^{19}.3^{19}-7.2^{29}.\left(3^3\right)^6}\)
=\(\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}3^{18}}=\dfrac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=2\)
b) Ta có \(B=\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}=\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.7^3.2^3}\)
\(=\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.2^3}=\dfrac{5^{10}.7^3\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}=\dfrac{-6}{9}=\dfrac{-2}{3}\)
Câu c mình chịu
a) Ta có: \(A=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{29}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}\)
\(=2\)
Ko nhìn rõ đề câu C lắm, nhất là 2 mũ của số 2 dưới mẫu không thể thấy được nó là số 8 hay số 3 nên đoán:
\(C=\dfrac{\left(3.2^2.2^{16}\right)^2}{11.2^{13}.2^{22}-2^{18}.2^{18}}=\dfrac{3^2.2^{36}}{11.2^{35}-2^{36}}=\dfrac{3^2.2^{36}}{2^{35}\left(11-2\right)}=\dfrac{9.2^{36}}{2^{35}.9}=2\)
