a) \(x + \frac{5}{6} = \frac{4}{3}\)

\(x = \frac{4}{3} - \frac{5}{6} = \frac{8}{6} - \frac{5}{6}\)

\(x = \frac{3}{6} = \frac{1}{2}\)

b) \(x : 2^{4} = 8^{3}\)

\(x : 2^{4} = \left(\right. 2^{3} \left.\right)^{3}\)

\(x : 2^{4} = 2^{9}\)

\(x = 2^{9} . 2^{4} = 2^{13}\)

c) \(\frac{13}{4} . \left(\right. \frac{5}{52} - x \left.\right) = \frac{1}{4}\)

\(\frac{5}{52} - x = \frac{1}{4} : \frac{13}{4}\)

\(\frac{5}{52} - x = \frac{1}{13}\)

\(x = \frac{5}{52} - \frac{1}{13}\)

\(x = \frac{1}{52}\)

a) \(\frac{5}{9} - \left(\left(\right. \frac{1}{3} \left.\right)\right)^{2} = \frac{5}{9} - \frac{1}{9} = \frac{4}{9}\)

b) \(\frac{1}{5}.\frac{-3}{2};+\frac{- 17}{2}.\frac{1}{5}\)

\(= \frac{1}{5} . \left(\right. \frac{- 3}{2} + \frac{- 17}{2} \left.\right)\)

\(= \frac{1}{5} . \left(\right. - 10 \left.\right) = - 2\)

c) \(1 + \left(\right. \frac{- 2}{5} + \frac{11}{13} \left.\right) - \left(\right. \frac{3}{5} - \frac{2}{13} \left.\right)\)

\(= 1 + \frac{- 2}{5} + \frac{11}{13} - \frac{3}{5} + \frac{2}{13}\)

\(= 1 + \left(\right. \frac{- 2}{5} - \frac{3}{5} \left.\right) + \left(\right. \frac{11}{13} + \frac{2}{13} \left.\right)\)

\(= 1 + \left(\right. - 1 \left.\right) + 1 = 1\)