Answer
(a) $\frac{\sqrt{5x}}{5x}$
(b) $\frac{\sqrt{5x}}{5}$
(c) $\frac{x^{2/5}}{x}$
Work Step by Step
(a) $\displaystyle \frac{1}{\sqrt{5x}}=\frac{1}{\sqrt{5x}} \displaystyle \frac{\sqrt{5x}}{\sqrt{5x}}=\frac{\sqrt{5x}}{5x}$
(b)$\displaystyle \sqrt{\frac{x}{5}}=\frac{\sqrt{x}}{\sqrt{5}} \displaystyle=\frac{\sqrt{x}}{\sqrt{5}} \displaystyle \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5x}}{5}$
(c) $\displaystyle \sqrt[5]{\frac{1}{x^{3}}}=\frac{1}{x^{3/5}} \displaystyle \frac{x^{2/5}}{x^{2/5}}=\frac{x^{2/5}}{x}$
