Bài 1:

\(a,\dfrac{4}{9}:\left(-\dfrac{1}{7}\right)+6\dfrac{5}{9}.\dfrac{2}{3}.\\ =\dfrac{-28}{9}+\dfrac{59}{9}.\dfrac{2}{3}=\dfrac{-28}{9}+\dfrac{118}{27}=\dfrac{34}{27}.\\ b,\left(\dfrac{-1}{3}\right)^2.\dfrac{4}{11}+\dfrac{7}{11}.\left(-\dfrac{1}{3}\right)^2.\\ =\left(\dfrac{-1}{3}\right)^2\left(\dfrac{4}{11}+\dfrac{7}{11}\right)=\dfrac{1}{9}.\)

Bài 3:

\(a,\left(\dfrac{1}{3}-\dfrac{5}{6}\right)^2+\dfrac{5}{6}:2.\\ =\left(-\dfrac{1}{2}\right)^2+\dfrac{5}{12}.\\ =\dfrac{1}{4}+\dfrac{5}{12}=\dfrac{2}{3}.\\ b,5,7+3,6-3\left(1,2-2,8\right).\\ =5,7+3,6-3,6+8,4.\\ =14,1.\):

\(\left(3x-5\right)^4=81.\\\Leftrightarrow\left[{}\begin{matrix}\left(3x-5\right)^4=3^4.\\\left(3x-5\right)^4=\left(-3\right)^4.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-5=3.\\3x-5=-3.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}.\\x=\dfrac{2}{3}.\end{matrix}\right.\)

\(\left(7-3x\right)^2+15=16.\\ \Leftrightarrow\left(7-3x\right)^2=1.\\ \Leftrightarrow\left[{}\begin{matrix}7-3x=1.\\7-3x=-1.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2.\\x=\dfrac{8}{3}.\end{matrix}\right.\)

\(\left(4-3x\right)^3+15=7.\\ \Leftrightarrow\left(4-3x\right)^3=-8.\\ \Leftrightarrow\left(4-3x\right)^3=\left(-2\right)^3.\\ \Leftrightarrow4-3x=-2.\\ \Leftrightarrow x=2.\)

\(\left(2x-3\right)^3-14=50.\\ \Leftrightarrow\left(2x-3\right)^3=64.\\ \Leftrightarrow\left(2x-3\right)^3=4^3.\\ \Leftrightarrow2x-3=4.\\ \Leftrightarrow x=\dfrac{7}{2}.\)

\(3^7-x=243.\\ \Leftrightarrow x=3^7-243=1944.\)

Bài 2:

\(a,\left(3\dfrac{1}{4}:x\right).\left(-1\dfrac{1}{4}\right)=-\dfrac{5}{3}-\dfrac{5}{6}.\\ \Leftrightarrow\left(\dfrac{13}{4}:x\right).\dfrac{-5}{4}=-\dfrac{5}{2}.\\ \Leftrightarrow\dfrac{13}{4}:x=2.\\ \Leftrightarrow x=\dfrac{13}{8}.\)

\(b,\dfrac{-1}{4}-\dfrac{3}{4}:x=-\dfrac{11}{36}.\\ \Leftrightarrow\dfrac{3}{4}:x=\dfrac{1}{18}.\\ \Leftrightarrow x=\dfrac{27}{2}.\)

Bài 3.

\(a,\left|x-1\right|=2x-5.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=2x-5.\\x-1=5-2x.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4.\\x=2.\end{matrix}\right.\)