a) Ta có: \(A=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}\)
\(=2\)
b) Ta có: \(B=\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
\(=\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^6}\)
\(=\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+7^3\right)}\)
\(=5\cdot\dfrac{-6}{344}\)
\(=\dfrac{-30}{344}=\dfrac{-15}{172}\)
c) Ta có: \(C=\dfrac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{18}\cdot4^{11}-4^9\cdot2^{10}}\)
\(=\dfrac{3^2\cdot2^{36}}{11\cdot2^{40}-2^{28}}\)
\(=\dfrac{2^{36}\cdot3^2}{2^{28}\left(11\cdot2^{12}-1\right)}\)
\(=2^8\cdot\dfrac{3^2}{45055}=\dfrac{2304}{45055}\)
