a) \(A=\dfrac{5\cdot7^{11}+7^{12}}{7^9\cdot5^2-7^9\cdot13}=\dfrac{7^{11}\left(5+7\right)}{7^9\cdot\left(5^2-13\right)}=7^2=49\)
b) \(B=\dfrac{2^{15}\cdot7-2^{16}}{5\cdot2^{15}}=\dfrac{2^{15}\left(7-2\right)}{2^{15}\cdot5}=1\)
c) \(C=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-4\cdot3^{20}\cdot2^{27}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{27}\cdot3^{18}\left(5\cdot2^3-4\cdot3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}\)
\(=\dfrac{5\cdot8-4\cdot9}{2}\)
\(=\dfrac{40-36}{2}=\dfrac{4}{2}=2\)
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