б) $$\sqrt{y^5\sqrt[9]{x^4y^2}}$$;

б) $$\sqrt{y^5\sqrt[9]{x^4y^2}}$$;

$$\sqrt{y^5\sqrt[9]{x^4y^2}} = \sqrt{y^5x^{\frac{4}{9}}y^{\frac{2}{9}}} = \sqrt{y^{\frac{45}{9}}x^{\frac{4}{9}}y^{\frac{2}{9}}} = \sqrt{x^{\frac{4}{9}}y^{\frac{47}{9}}} = x^{\frac{4}{9*2}}y^{\frac{47}{9*2}} = x^{\frac{2}{9}}y^{\frac{47}{18}} = \sqrt[9]{x^2}\cdot \sqrt[18]{y^{47}} = \sqrt[9]{x^2}\cdot \sqrt[18]{y^{36+11}} = \sqrt[9]{x^2}\cdot \sqrt[18]{y^{36}}\cdot \sqrt[18]{y^{11}} = \sqrt[9]{x^2}\cdot y^{\frac{36}{18}}\cdot \sqrt[18]{y^{11}} = y^2\sqrt[9]{x^2}\cdot \sqrt[18]{y^{11}}$$

Ответ: $$y^2\sqrt[9]{x^2}\cdot \sqrt[18]{y^{11}}$$