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Các thừa số lập đi là 2 và 3 (số mũ nhỏ nhất)
< = > UCLN(a , b ,c) = 2.3 = 6
\(\frac{2^5\times7+2^5}{2^5\times5^2-2^5\times3}=\frac{2^5\times\left(7-1\right)}{2^5\times25-2^5\times3}=\frac{2^5\times8}{2^5\times\left(25-3\right)}=\frac{2^5\times8}{2^5\times22}=\frac{8}{22}=\frac{4}{11}\)
\(\frac{2^5x7+2^5}{2^5x5^2-2^5x3}\)= \(\frac{2^5\left(7+1\right)}{2^5\left(5^2-3\right)}\)= \(\frac{2^5.8}{2^5.22}\)=\(\frac{8}{22}\)=\(\frac{4}{11}\)
Bài làm
\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{x.\left(x+2\right)}=\frac{2015}{2016}\)
\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{x}-\frac{1}{x+2}=\frac{2015}{2016}\)
\(1-\frac{1}{x+2}=\frac{2015}{2016}\)
\(\frac{1}{x+2}=\frac{1}{2016}\)
\(\Rightarrow x+2=2016\)
\(x=2014\)
\(a)\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{-11.13^7}{11^5.13^8}=\frac{-1}{11^4.13}\) (Bạn xem thử xem có sai đề không nhé)
\(c)\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3+1\right)}{2^9.3^{10}}=\frac{2.4}{3}=\frac{8}{3}\)
\(d)\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.4+9\right)}=\frac{8}{20+9}=\frac{8}{29}\)
\(a)\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{\left(-11\right)\cdot13^7}{11^5\cdot13^8}=\frac{-1}{11^4\cdot13}=\frac{-1}{14641\cdot13}=\frac{-1}{190333}\)
\(c)\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^{10}\left(3^{10}-3^9\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\cdot2}{2^9\cdot3^{10}}=\frac{2\cdot2}{3}=\frac{4}{3}\)
\(\left(2^3.3^5.5^7\right)^{10}.12^{20}\)
\(=2^{30}.3^{50}.5^{70}.\left(2^2.3\right)^{20}\)
\(=2^{30}.3^{50}.5^{70}.2^{40}.3^{20}\)
\(=2^{70}.3^{70}.5^{70}=\left(30\right)^{70}\)