To simplify the expression (-2/3)² + 4(1/3)³, we first need to evaluate each term separately.

(-2/3)² = (-2/3) * (-2/3) = 4/9

(1/3)³ = (1/3) * (1/3) * (1/3) = 1/27

Now we can substitute these values back into the original expression:

(-2/3)² + 4(1/3)³ = 4/9 + 4/27

To add these fractions, we need a common denominator. The least common multiple of 9 and 27 is 27, so we can rewrite the fractions with this denominator:

4/9 + 4/27 = (4/9)(3/3) + (4/27)(1/1) = 12/27 + 4/27

Now that the fractions have the same denominator, we can add them:

12/27 + 4/27 = 16/27

Therefore, (-2/3)² + 4(1/3)³ simplifies to 16/27.