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$\small \left(ab-\dfrac{2}{3}ab\right)b^3 -a\left(-b^2\right)^3 : \left(-\dfrac{1}{3}b\right)^2+\dfrac{2}{3}ab^4 =$
$\small =\left(\dfrac{3-2}{3}ab\right)b^3 -a\left(-b^{2×3}\right) : \dfrac{1}{9}b^2+\dfrac{2}{3}ab^4 =$
$\small =\left(\dfrac{1}{3}ab\right)b^3 -a\left(-b^6\right) · 9b^{-2}+\dfrac{2}{3}ab^4 =$
$\small =\dfrac{1}{3}ab^4 +ab^6 · 9b^{-2}+\dfrac{2}{3}ab^4 =$
$\small =\dfrac{1}{3}ab^4 +9ab^{6+(-2)} +\dfrac{2}{3}ab^4 =$
$\small =\dfrac{1}{3}ab^4 +9ab^{6-2} +\dfrac{2}{3}ab^4 =$
$\small =\dfrac{1}{3}ab^4 +9ab^4 +\dfrac{2}{3}ab^4 =$
$\small = \dfrac{1+27+2}{3}ab^4 =$
$\small = \dfrac{\cancel{30}^{10}}{\cancel3_1}ab^4 =$
$\small = 10ab^4$
ab^4 - 2/3 ab^4 - a * (- b^6) : (+ 1/9 b^2) + 2/3 ab^4 =
(- 2/3 ab^4 + 2/3 ab^4 = 0; monomi opposti).
= ab^4 + ab^6 : (+ 1/9 b^2 =
= ab^4 + a b^6 * (9 / b^2) =
= a b^4 + 9 a b^4 = 10 a b^4.
Ciao @kezy