Answer
(a) $\frac{\sqrt{3st}}{3t}$
(b) $\frac{ab^{2/3}}{b}$
(c) $\frac{c^{2/5}}{c}$
Work Step by Step
(a) $(\displaystyle \mathrm{a})\sqrt{\frac{s}{3t}}=\frac{\sqrt{s}}{\sqrt{3t}} \displaystyle \frac{\sqrt{3t}}{\sqrt{3t}}=\frac{\sqrt{3st}}{3t}$
(b) $\displaystyle \frac{a}{\sqrt[6]{b^{2}}}=\frac{a}{b^{1/3}} \displaystyle =\frac{a}{b^{1/3}} \displaystyle \frac{b^{2/3}}{b^{2/3}}=\frac{ab^{2/3}}{b}$
(c) $\displaystyle \frac{1}{c^{3/5}}=\frac{1}{c^{3/5}} \displaystyle \frac{c^{2/5}}{c^{2/5}}=\frac{c^{2/5}}{c}$
