10. Найдите значение выражения √81/b / √b при b > 0.

Ответ: 9

\[ \frac{\sqrt{\frac{81}{\sqrt{b}}}}{\sqrt{b}} = \frac{\sqrt{81}}{\sqrt{\sqrt{b}} \cdot \sqrt{b}} = \frac{9}{\sqrt[4]{b} \cdot \sqrt{b}} \] \[ \frac{\sqrt{\frac{81}{\sqrt{b}}}}{\sqrt{b}} = \frac{\sqrt{81}}{\sqrt{\sqrt{b}} \cdot \sqrt{b}} = \frac{9}{b^{\frac{1}{4}} \cdot b^{\frac{1}{2}}} = \frac{9}{b^{\frac{3}{4}}} \] \[\frac{\sqrt{\frac{81}{\sqrt{b}}}}{\sqrt{b}} = \frac{\sqrt{81}}{\sqrt{\sqrt{b}} \cdot \sqrt{b}} = \frac{9}{\sqrt{\sqrt{b} \cdot b}} = \frac{9}{\sqrt{b^{\frac{3}{2}}}} = \frac{9}{b^{\frac{3}{4}}}\]

Ответ: 9