Answer:
[tex]\dfrac{145}{144}[/tex]
Step-by-step explanation:
Use PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
[tex]\left ( \dfrac{1}{4}+\dfrac{1}{3}\right)^2+\dfrac{2}{3}\\=\left ( \dfrac{1}{4}\times \dfrac{3}{3}+\dfrac{1}{3}\times \dfrac{4}{4}\right)^2+\dfrac{2}{3}\\\\=\left ( \dfrac{3}{12}+\dfrac{4}{12}\right)^2+\dfrac{2}{3}\\=\left ( \dfrac{3+4}{12}\right)^2+\dfrac{2}{3}\\\\=\left ( \dfrac{7}{12}\right)^2+\dfrac{2}{3}\\=\dfrac{49}{144}+\dfrac{2}{3}\times \dfrac{48}{48}\\=\dfrac{49}{144}+\dfrac{96}{144}\\=\dfrac{145}{144}[/tex]
