19) (a20.a*): an = a12 (a2)2

19) $$\frac{(a^{20} \cdot a^4) : a^{4n}}{(a^2)^2} = a^{12}$$ $$\frac{a^{24} : a^{4n}}{a^4} = a^{12}$$ $$\frac{a^{24-4n}}{a^4} = a^{12}$$ $$a^{24 - 4n - 4} = a^{12}$$ $$a^{20 - 4n} = a^{12}$$ Следовательно, $$20 - 4n = 12$$ $$-4n = 12 - 20$$ $$-4n = -8$$ $$4n = 8$$ $$n = 8 : 4$$ $$n = 2$$

Ответ: 2