3) \(\sqrt{81a^7}-5a^3\sqrt a+\frac{6}{a}\sqrt{a^9}\).

При \(a>0\): \(\sqrt{81a^7}=9a^3\sqrt a\), а \(\sqrt{a^9}=a^4\sqrt a\).

\(\sqrt{81a^7}-5a^3\sqrt a+\frac{6}{a}\sqrt{a^9}=9a^3\sqrt a-5a^3\sqrt a+\frac{6}{a}\cdot a^4\sqrt a\).

\(=(9-5+6)a^3\sqrt a=10a^3\sqrt a\).

Ответ: \(10a^3\sqrt a\), \(a>0\).