Question

0,5.4/9+(1/3-1,5)²-(2/3)⁹:(2/3)⁷

Answer 1

\(0,5\times\dfrac{4}{9}+\left(\dfrac{1}{3}-1,5\right)^2-\left(\dfrac{2}{3}\right)^9:\left(\dfrac{2}{3}\right)^7\\ =\dfrac{1}{2}\times\dfrac{4}{9}+\left(\dfrac{1}{3}-\dfrac{3}{2}\right)^2-\left(\dfrac{2}{3}\right)^{9-7}\\ =\dfrac{2}{9}+\left(\dfrac{2-3.3}{6}\right)^2-\left(\dfrac{2}{3}\right)^2\\ =\dfrac{2}{9}+\left(-\dfrac{7}{6}\right)^2-\dfrac{4}{9}\\ =\dfrac{2}{9}+\dfrac{49}{36}-\dfrac{4}{9}\\ =-\dfrac{2}{9}+\dfrac{49}{36}\\ =\dfrac{-2\times4+49}{36}\\ =\dfrac{-8+49}{36}\\ =\dfrac{41}{36}\)