Just multiply 1/6 to every exponent in the expression:
[tex](8 a^{3} b^{6})^ \frac{1}{6} [/tex]
⇓
[tex](2^3a^{3} b^{6})^ \frac{1}{6} [/tex]
⇓
[tex]2^{(3)\frac{1}{6}} a^{(3)\frac{1}{6} } b^{(6)\frac{1}{6} }[/tex]
⇓
[tex]2^ \frac{1}{2} a^{\frac{1}{2}} b^{1}[/tex]
⇓
[tex](2a)^ \frac{1}{2} b= \boxed{b \sqrt{2a} }[/tex]
