3. Упростите: 1) $$\frac{13x^{-4}}{y^{-6}} \cdot \frac{y}{52x^{-5}}$$ 2) $$\frac{21a^{-4}}{10b^{6}} : \frac{5b^{-6}}{7a^{-8}}$$

Решение:

• 1) $$\frac{13x^{-4}}{y^{-6}} \cdot \frac{y}{52x^{-5}} = \frac{13x^{-4} \cdot y}{y^{-6} \cdot 52x^{-5}} = \frac{13}{52} \cdot \frac{x^{-4}}{x^{-5}} \cdot \frac{y}{y^{-6}} = \frac{1}{4} \cdot x^{-4 - (-5)} \cdot y^{1 - (-6)} = \frac{1}{4} \cdot x^{-4+5} \cdot y^{1+6} = \frac{1}{4} x¹ y⁷ = \frac{xy⁷}{4}$$
• 2) $$\frac{21a^{-4}}{10b^{6}} : \frac{5b^{-6}}{7a^{-8}} = \frac{21a^{-4}}{10b^{6}} \cdot \frac{7a^{-8}}{5b^{-6}} = \frac{21 \cdot 7 \cdot a^{-4} \cdot a^{-8}}{10 \cdot 5 \cdot b^{6} \cdot b^{-6}} = \frac{147 \cdot a^{-4+(-8)}}{50 \cdot b^{6+(-6)}} = \frac{147 a^{-12}}{50 b^{0}} = \frac{147}{50a^{12}}$$

Ответ: 1) $$\frac{xy⁷}{4}$$; 2) $$\frac{147}{50a^{12}}$$