2/11 của -33/3
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a) 2/3 + 3/4 . (-4/9)
= 2/3 - 1/3
= 1/3
b) -5/7 . 31/33 + (-5/7) : 33/2
= -5/7 . 31/33 - 5/7 . 2/33
= -5/7 . (31/33 + 2/33)
= -5/7 . 1
= -5/7
c) -3/5 . 13/11 - (-3/5) . 2/11
= -3/5 . (13/11 - 2/11)
= -3/5 . 1
= -3/5
\(=\dfrac{3^{10}.33+\left(-3\right)^{11}.\left(-21\right)}{3^9.2^5}\\ =\dfrac{3^{10}.3.11+3^{11}.3.7}{3^9.2^5}\\ =\dfrac{3^{11}.11+3^{12}.7}{3^9.2^5}\\ =\dfrac{3^9\left(3^2.11+3^3.7\right)}{3^9.2^5}\\ =\dfrac{\left(9.11+27.7\right)}{2^5}\\ =\dfrac{99+189}{32}\\ =\dfrac{288}{32}=9\)
\(\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\left(\dfrac{10}{-33}.\dfrac{11}{8}\right).\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{-5}{12}.\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{2}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{2}{11}-\dfrac{1}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{1}{11}\)
\(\Rightarrow x=\dfrac{1}{11}-\dfrac{2}{3}\)
\(\Rightarrow x=-\dfrac{19}{33}\)
\(\Leftrightarrow\left(11+\dfrac{7}{18}-9-\dfrac{13}{18}\right):x=\dfrac{5}{3}+\dfrac{35}{33}\cdot\dfrac{11}{7}=\dfrac{10}{3}\)
\(\Leftrightarrow x=\dfrac{5}{3}:\dfrac{10}{3}=\dfrac{1}{2}\)