[tex] \frac{3}{5a} \sqrt{5 {a}^{6} } = \sqrt{ \frac{ {3}^{2} \times 5 {a}^{6} }{5 {}^{2} \times {a}^{2} } } = \sqrt{ \frac{9 {a}^{4} }{5} } [/tex]

[tex] \frac{1}{9} \sqrt{81} = \sqrt{ \frac{81}{ {9}^{2} } } = \sqrt{ \frac{81}{81} } = \sqrt{1} = 1[/tex]