Задание 3. Найдите значение выражения:

1. $\frac{\sqrt{25a^9}\cdot\sqrt{16b^8}}{\sqrt{a^5b^8}} = \frac{5a^{4.5}\cdot4b^4}{a^{2.5}b^4} = \frac{5a^{4.5}\cdot4}{a^{2.5}} = 20a^2 = 20\cdot4^2 = 320$ 2. $\frac{\sqrt{16a^9}\cdot\sqrt{4b^3}}{\sqrt{a^5b^3}} = \frac{4a^{4.5}\cdot2b^{1.5}}{a^{2.5}b^{1.5}} = \frac{4a^{4.5}\cdot2}{a^{2.5}} = 8a^2 = 8\cdot9^2 = 648$ 3. $\frac{\sqrt{4a^{11}}\cdot\sqrt{9b^4}}{\sqrt{a^7b^4}} = \frac{2a^{5.5}\cdot3b^2}{a^{3.5}b^2} = \frac{2a^{5.5}\cdot3}{a^{3.5}} = 6a^2 = 6\cdot7^2 = 294$ 4. $\frac{\sqrt{25a^5}\cdot\sqrt{36b^6}}{\sqrt{a^5b^4}} = \frac{5a^{2.5}\cdot6b^3}{a^{2.5}b^2} = \frac{5\cdot6b}{1} = 30b = 30\cdot9 = 270$ 5. $\frac{\sqrt{16a^5}\cdot\sqrt{36b}}{\sqrt{ab}} = \frac{4a^{2.5}\cdot6b^{0.5}}{a^{0.5}b^{0.5}} = \frac{4a^{2.5}\cdot6}{a^{0.5}} = 24a^2 = 24\cdot7^2 = 1176$ 6. $\frac{\sqrt{4a^6}\cdot\sqrt{25b^7}}{\sqrt{a^2b^7}} = \frac{2a^3\cdot5b^{3.5}}{a^1b^{3.5}} = \frac{2a^3\cdot5}{a^1} = 10a^2 = 10\cdot9^2 = 810$ 7. $\frac{\sqrt{36a}\cdot\sqrt{9b^5}}{\sqrt{ab}} = \frac{6a^{0.5}\cdot3b^{2.5}}{a^{0.5}b^{0.5}} = \frac{6\cdot3b^2}{1} = 18b^2 = 18\cdot4^2 = 288$ 8. $\frac{\sqrt{25a^8}\cdot\sqrt{9b^5}}{\sqrt{a^4b^5}} = \frac{5a^4\cdot3b^{2.5}}{a^2b^{2.5}} = \frac{5a^4\cdot3}{a^2} = 15a^2 = 15\cdot7^2 = 735$ 9. $\sqrt{\frac{1}{16}x^6y^4} = \frac{1}{4}x^3y^2 = \frac{1}{4}\cdot2^3\cdot5^2 = \frac{1}{4}\cdot8\cdot25 = 50$ 10. $\sqrt{\frac{1}{25}x^8y^2} = \frac{1}{5}x^4y = \frac{1}{5}\cdot3^4\cdot5 = 81$ 11. $\sqrt{\frac{1}{4}x^2y^8} = \frac{1}{2}xy^4 = \frac{1}{2}\cdot5\cdot2^4 = \frac{1}{2}\cdot5\cdot16 = 40$ 12. $\sqrt{\frac{1}{9}x^4y^{10}} = \frac{1}{3}x^2y^5 = \frac{1}{3}\cdot3^2\cdot2^5 = \frac{1}{3}\cdot9\cdot32 = 96$ 13. $\sqrt{\frac{1}{4}x^8y^4} = \frac{1}{2}x^4y^2 = \frac{1}{2}\cdot2^4\cdot3^2 = \frac{1}{2}\cdot16\cdot9 = 72$ 14. $\sqrt{\frac{1}{25}x^4y^8} = \frac{1}{5}x^2y^4 = \frac{1}{5}\cdot5^2\cdot2^4 = \frac{1}{5}\cdot25\cdot16 = 80$ 15. $\sqrt{\frac{1}{9}x^2y^6} = \frac{1}{3}xy^3 = \frac{1}{3}\cdot7\cdot3^3 = \frac{1}{3}\cdot7\cdot27 = 63$ 16. $\sqrt{\frac{1}{16}x^{10}y^2} = \frac{1}{4}x^5y = \frac{1}{4}\cdot2^5\cdot3 = \frac{1}{4}\cdot32\cdot3 = 24$