6. Упростите выражение: а) 3/7x⁵y⁶ · (-2/3x⁵y)²; б) (aⁿ⁺¹)² : a²ⁿ.

1. a) $$\frac{3}{7}x^5y^6 \cdot \left(-\frac{2}{3}x^5y\right)^2 = \frac{3}{7}x^5y^6 \cdot \frac{4}{9}x^{10}y^2 = \frac{3 \cdot 4}{7 \cdot 9}x^{5+10}y^{6+2} = \frac{12}{63}x^{15}y^8 = \frac{4}{21}x^{15}y^8$$
2. б) $$\frac{(a^{n+1})^2}{a^{2n}} = \frac{a^{2(n+1)}}{a^{2n}} = \frac{a^{2n+2}}{a^{2n}} = a^{2n+2-2n} = a^2$$

Ответ: a) $$\frac{4}{21}x^{15}y^8$$, б) $$a^2$$