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[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big[\dfrac{4}{3}-(0,(3))^{2}\Big]:4\dfrac{8}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big[\dfrac{4}{3}-\Big(\dfrac{3}{9}\Big)^{2}\Big]:\dfrac{4\cdot9+8}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big[\dfrac{4}{3}-\Big(\dfrac{\not3}{\not9}\Big)^{2}\Big]:\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big[\dfrac{4}{3}-\Big(\dfrac{1}{3}\Big)^{2}\Big]:\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big(\dfrac{4}{3}-\dfrac{1}{9}\Big):\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\Big(\dfrac{4\cdot3}{3\cdot3}-\dfrac{1}{9}\Big):\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\dfrac{12-1}{9}:\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\dfrac{11}{9}:\dfrac{44}{9}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{4}{3}\cdot\dfrac{11}{9}\cdot\dfrac{9}{44}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{\not4}{3}\cdot\dfrac{\not11}{\not9}\cdot\dfrac{\not9}{\not44}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{1}{3}\cdot\dfrac{1}{1}\cdot\dfrac{1}{1}[/tex]
[tex]\bf n = \dfrac{4}{3}- \dfrac{1}{3}[/tex]
[tex]\bf n = \dfrac{4-1}{3}[/tex]
[tex]\bf n = \dfrac{3}{3}[/tex]
[tex]\bf n = \dfrac{\not3}{\not3}[/tex]
[tex]\boxed{\bf n = 1}[/tex]
