\(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\times-\dfrac{7}{11}=\dfrac{-5}{11}\)

5/7 x ( 5/11 + 2/11 - 14/11) = 5/7 x -7/11 = -5/11

5/7×5/11+5/7×2/11-5/7×14/11

= 5/7 x ( 5/11 + 2/11 - 14/11 )

= 5/7 x -7/11

= -35/77

sai

\(=\dfrac{5}{11}\left(-\dfrac{3}{7}-\dfrac{5}{7}\right)+\dfrac{-8}{7}\cdot\dfrac{6}{11}=\dfrac{-8}{7}\left(\dfrac{5}{11}+\dfrac{6}{11}\right)=-\dfrac{8}{7}\)

\(\dfrac{5}{11}.\left(-\dfrac{3}{7}\right)+\dfrac{5}{11}.\left(-\dfrac{5}{7}\right)+\left(-\dfrac{8}{7}\right).\dfrac{6}{11}\)

\(=\dfrac{5}{11}.\left[-\dfrac{3}{7}+\left(-\dfrac{5}{7}\right)\right]+\left(-\dfrac{8}{7}\right).\dfrac{6}{11}\)

\(=\dfrac{5}{11}.\left(-\dfrac{8}{7}\right)+\left(-\dfrac{8}{7}\right).\dfrac{6}{11}=\left(\dfrac{5}{11}+\dfrac{6}{11}\right).\left(-\dfrac{8}{7}\right)\)

\(=1.\left(-\dfrac{8}{7}\right)=-\dfrac{8}{7}\)

a: \(\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-3^{10}\cdot5^{21}}{3^{12}\cdot5^{20}}=\frac{-5}{3^2}=-\frac59\)

b: \(\frac{-11^5\cdot13^7}{11^5\cdot13^8}=\frac{-11^5}{11^5}\cdot\frac{13^7}{13^8}=-\frac{1}{13}\)

c: \(2^{10}\cdot3^{10}-2^{10}\cdot3^9\)

\(=2^{10}\cdot3^9\cdot\left(3-1\right)\)

\(=2^{11}\cdot3^9\)

Ta có: \(\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}\)

\(=\frac{2^{11}\cdot3^9}{2^{10}\cdot3^9}=2\)

d: \(5^{11}\cdot7^{12}+5^{11}\cdot7^{11}\)

\(=5^{11}\cdot7^{11}\left(7+1\right)=5^{11}\cdot7^{11}\cdot8\)

\(5^{12}\cdot7^{12}+9\cdot5^{11}\cdot7^{11}\)

\(=5^{11}\cdot7^{11}\left(5\cdot7+9\right)\)

\(=5^{11}\cdot7^{11}\left(35+9\right)=5^{11}\cdot7^{11}\cdot44\)

Ta có: \(\frac{5^{11}\cdot7^{12}+5^{11}\cdot7^{11}}{5^{12}\cdot7^{12}+9\cdot5^{11}\cdot7^{11}}\)

\(=\frac{5^{11}\cdot7^{11}\cdot8}{5^{11}\cdot7^{11}\cdot44}=\frac{8}{44}=\frac{2}{11}\)

\(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}\)

=\(\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.7+9\right)}\)

= \(\frac{8}{35+9}\)

= \(\frac{8}{44}\)

= \(\frac{2}{11}\)

5 12 .7 12 +9.5 11 .7 11 5 11 .7 12 +5 11 .7 11 = 5 11 . 7 11 ( 7 + 1 ) 5 11 . 7 11 ( 5.7 + 9 ) 5 11 .7 11 (5.7+9) 5 11 .7 11 (7+1) = 8 35 + 9 35+9 8 = 8 44 44 8 = 2 11 11 2

\(\frac{5^{11}\cdot7^{12}+5^{11}\cdot7^{11}}{5^{12}\cdot7^{11}+9\cdot5^{11}\cdot7^{11}}\)

=\(\frac{5^{11}\cdot\left(7^{12}+7^{11}\right)}{5^{11}\left(5\cdot7^{11}+9\cdot7^{11}\right)}\)

=\(\frac{7^{12}+7^{11}}{5\cdot7^{11}+9\cdot7^{11}}\)

=\(\frac{7^{11}\left(7+1\right)}{7^{11}\left(5+9\right)}\)

=\(\frac{8}{14}=\frac{4}{7}\)

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tính theo công thức bạn nhé

\(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{8}{11}-\dfrac{5}{7}.\dfrac{2}{11}\)

= \(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{8}{11}-\dfrac{2}{11}\right)\)

= \(\dfrac{5}{7}.\dfrac{5+8-2}{11}\)

= \(\dfrac{5}{7}.\dfrac{11}{11}\)

= \(\dfrac{5}{7}.1=\dfrac{5}{7}\)