Answer
$\dfrac{1}{9}$
Work Step by Step
RECALL:
(i) For any non-negative real numbers $a$ and $b$,
$\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}$ and $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$.
(ii) For any non-negative real number $a$, $\sqrt{a^2}=a$.
Use rule (i) above to obtain
$\dfrac{\sqrt{1}}{\sqrt{81}}
\\=\dfrac{1}{\sqrt{9^2}}.$
Use rule (ii) above to obtain
$\dfrac{1}{9}.$
