[tex]\bf =\bigg(\dfrac{2^2}{3^2}\bigg)^{10} \cdot\bigg(\dfrac{3^3}{2^3}\bigg)^{6}+1 =\bigg(\dfrac{2}{3}\bigg)^{20} \cdot\bigg(\dfrac{3}{2}\bigg)^{18}+1=\\ \\ \\ =\bigg(\dfrac{2}{3}\bigg)^{2}\cdot\bigg(\dfrac{2}{3}\bigg)^{18}\cdot\bigg(\dfrac{3}{2}\bigg)^{18}+1=\dfrac{4}{9}\cdot\bigg(\dfrac{\not2\ ^1}{\not3}\cdot\dfrac{\not3}{\not2}\bigg)^{18}+1=\dfrac{4}{9}+1=1\dfrac{4}{9}\\ \\ \\[/tex]
