a) $$y^6 \cdot \left(-2 \frac{1}{3}x^5y\right)^2 = y^6 \cdot \left(-\frac{7}{3}x^5y\right)^2 = y^6 \cdot \left(\frac{49}{9}x^{5 \cdot 2}y^2\right) = \frac{49}{9}x^{10}y^{6+2} = \frac{49}{9}x^{10}y^8$$
б) $$(a^{n+1})^2 : a^{2n} = a^{2(n+1)} : a^{2n} = a^{2n+2} : a^{2n} = a^{2n+2-2n} = a^2$$
Ответ: a) $$\frac{49}{9}x^{10}y^8$$, б) $$a^2$$