109. Представьте в виде дроби: a) $$\frac{7a^2x^2}{4y^3} : \frac{35a^3x^3}{8y^4}$$; B) $$\frac{42x^6}{17y^6} : (-\frac{21x^5}{51y^5})$$; д) $$\frac{48x^{12}}{y^{16}} : (-16x^{10}y^4)$$; б) $$\frac{9ac}{13b} : \frac{18ab}{52c}$$; г) $$\frac{-p^{10}}{q^{10}} : \frac{3p^5}{2q^5}$$; e) $$\frac{37a^8b}{c^3} : (-\frac{111a^7b^2}{c^2})$$;

a)

$$\frac{7a^2x^2}{4y^3} : \frac{35a^3x^3}{8y^4} = \frac{7a^2x^2}{4y^3} \cdot \frac{8y^4}{35a^3x^3} = \frac{7 \cdot 8 \cdot a^2 \cdot x^2 \cdot y^4}{4 \cdot 35 \cdot a^3 \cdot x^3 \cdot y^3} = \frac{56a^2x^2y^4}{140a^3x^3y^3} = \frac{2y}{5ax}$$

Ответ: $$\frac{2y}{5ax}$$

б)

$$-\frac{9ac}{13b} : \frac{18ab}{52c} = -\frac{9ac}{13b} \cdot \frac{52c}{18ab} = -\frac{9 \cdot 52 \cdot ac \cdot c}{13 \cdot 18 \cdot b \cdot a \cdot b} = -\frac{468ac^2}{234ab^2} = -\frac{2c^2}{b^2}$$

Ответ: $$\frac{-2c^2}{b^2}$$

в)

$$\frac{42x^6}{17y^6} : (-\frac{21x^5}{51y^5}) = \frac{42x^6}{17y^6} \cdot (-\frac{51y^5}{21x^5}) = -\frac{42 \cdot 51 \cdot x^6 \cdot y^5}{17 \cdot 21 \cdot y^6 \cdot x^5} = -\frac{2142x^6y^5}{357x^5y^6} = -\frac{6x}{y}$$

Ответ: $$\frac{-6x}{y}$$

г)

$$-\frac{p^{10}}{q^{10}} : \frac{3p^5}{2q^5} = -\frac{p^{10}}{q^{10}} \cdot \frac{2q^5}{3p^5} = -\frac{2 \cdot p^{10} \cdot q^5}{3 \cdot q^{10} \cdot p^5} = -\frac{2p^5}{3q^5}$$

Ответ: $$\frac{-2p^5}{3q^5}$$

д)

$$\frac{48x^{12}}{y^{16}} : (-16x^{10}y^4) = \frac{48x^{12}}{y^{16}} \cdot \frac{1}{-16x^{10}y^4} = \frac{48x^{12}}{-16x^{10}y^{16}y^4} = \frac{48x^{12}}{-16x^{10}y^{20}} = -\frac{3x^2}{y^{20}}$$

Ответ: $$\frac{-3x^2}{y^{20}}$$

e)

$$\frac{37a^8b}{c^3} : (-\frac{111a^7b^2}{c^2}) = \frac{37a^8b}{c^3} \cdot (-\frac{c^2}{111a^7b^2}) = -\frac{37 \cdot a^8 \cdot b \cdot c^2}{111 \cdot a^7 \cdot b^2 \cdot c^3} = -\frac{37a^8bc^2}{111a^7b^2c^3} = -\frac{a}{3bc}$$

Ответ: $$\frac{-a}{3bc}$$