Задание 3. Найдите значение выражения:

1. $\frac{\sqrt{25a^9} \cdot \sqrt{16b^8}}{\sqrt{a^5b^8}} = \sqrt{\frac{25a^9 \cdot 16b^8}{a^5b^8}} = \sqrt{400a^4} = 20a^2 = 20 \cdot 4^2 = 20 \cdot 16 = 320$ 2. $\frac{\sqrt{16a^9} \cdot \sqrt{4b^3}}{\sqrt{a^5b^3}} = \sqrt{\frac{16a^9 \cdot 4b^3}{a^5b^3}} = \sqrt{64a^4} = 8a^2 = 8 \cdot 9^2 = 8 \cdot 81 = 648$ 3. $\frac{\sqrt{4a^{11}} \cdot \sqrt{9b^4}}{\sqrt{a^7b^4}} = \sqrt{\frac{4a^{11} \cdot 9b^4}{a^7b^4}} = \sqrt{36a^4} = 6a^2 = 6 \cdot 7^2 = 6 \cdot 49 = 294$ 4. $\frac{\sqrt{25a^5} \cdot \sqrt{36b^6}}{\sqrt{a^5b^4}} = \sqrt{\frac{25a^5 \cdot 36b^6}{a^5b^4}} = \sqrt{900b^2} = 30b = 30 \cdot 9 = 270$ 5. $\frac{\sqrt{16a^5} \cdot \sqrt{36b}}{\sqrt{ab}} = \sqrt{\frac{16a^5 \cdot 36b}{ab}} = \sqrt{576a^4} = 24a^2 = 24 \cdot 7^2 = 24 \cdot 49 = 1176$ 6. $\frac{\sqrt{4a^6} \cdot \sqrt{25b^7}}{\sqrt{a^2b^7}} = \sqrt{\frac{4a^6 \cdot 25b^7}{a^2b^7}} = \sqrt{100a^4} = 10a^2 = 10 \cdot 9^2 = 10 \cdot 81 = 810$ 7. $\frac{\sqrt{36a} \cdot \sqrt{9b^5}}{\sqrt{ab}} = \sqrt{\frac{36a \cdot 9b^5}{ab}} = \sqrt{324b^4} = 18b^2 = 18 \cdot 4^2 = 18 \cdot 16 = 288$ 8. $\frac{\sqrt{25a^8} \cdot \sqrt{9b^5}}{\sqrt{a^4b^5}} = \sqrt{\frac{25a^8 \cdot 9b^5}{a^4b^5}} = \sqrt{225a^4} = 15a^2 = 15 \cdot 7^2 = 15 \cdot 49 = 735$ 9. $\sqrt{\frac{1}{16} x^6 y^4} = \sqrt{\frac{1}{16} \cdot x^6 y^4} = \frac{1}{4} x^3 y^2 = \frac{1}{4} \cdot 2^3 \cdot 5^2 = \frac{1}{4} \cdot 8 \cdot 25 = 2 \cdot 25 = 50$ 10. $\sqrt{\frac{1}{25} x^8 y^2} = \sqrt{\frac{1}{25} \cdot x^8 y^2} = \frac{1}{5} x^4 y = \frac{1}{5} \cdot 3^4 \cdot 5 = 81$ 11. $\sqrt{\frac{1}{4} x^2 y^8} = \sqrt{\frac{1}{4} \cdot x^2 y^8} = \frac{1}{2} x y^4 = \frac{1}{2} \cdot 5 \cdot 2^4 = \frac{1}{2} \cdot 5 \cdot 16 = 5 \cdot 8 = 40$ 12. $\sqrt{\frac{1}{9} x^4 y^{10}} = \sqrt{\frac{1}{9} \cdot x^4 y^{10}} = \frac{1}{3} x^2 y^5 = \frac{1}{3} \cdot 3^2 \cdot 2^5 = \frac{1}{3} \cdot 9 \cdot 32 = 3 \cdot 32 = 96$ 13. $\sqrt{\frac{1}{4} x^8 y^4} = \sqrt{\frac{1}{4} \cdot x^8 y^4} = \frac{1}{2} x^4 y^2 = \frac{1}{2} \cdot 2^4 \cdot 3^2 = \frac{1}{2} \cdot 16 \cdot 9 = 8 \cdot 9 = 72$ 14. $\sqrt{\frac{1}{25} x^4 y^8} = \sqrt{\frac{1}{25} \cdot x^4 y^8} = \frac{1}{5} x^2 y^4 = \frac{1}{5} \cdot 5^2 \cdot 2^4 = \frac{1}{5} \cdot 25 \cdot 16 = 5 \cdot 16 = 80$ 15. $\sqrt{\frac{1}{9} x^2 y^6} = \sqrt{\frac{1}{9} \cdot x^2 y^6} = \frac{1}{3} x y^3 = \frac{1}{3} \cdot 7 \cdot 3^3 = \frac{1}{3} \cdot 7 \cdot 27 = 7 \cdot 9 = 63$ 16. $\sqrt{\frac{1}{16} x^{10} y^2} = \sqrt{\frac{1}{16} \cdot x^{10} y^2} = \frac{1}{4} x^5 y = \frac{1}{4} \cdot 2^5 \cdot 3 = \frac{1}{4} \cdot 32 \cdot 3 = 8 \cdot 3 = 24$