Answer
(a) $\displaystyle\frac{\sqrt[3]{x}}{x}$
(b) $\displaystyle\frac{\sqrt[4]{x}}{x}$
(c) $\displaystyle\frac{\sqrt[3]{x^{2}}}{x^{2}}$
Work Step by Step
(a) $\displaystyle \frac{1}{\sqrt[3]{x^{2}}}=\frac{1}{\sqrt[3]{x^{2}}} \displaystyle \frac{\sqrt[3]{x}}{\sqrt[3]{x}}=\frac{\sqrt[3]{x}}{x}$
(b) $\displaystyle \frac{1}{\sqrt[4]{x^{3}}}=\frac{1}{\sqrt[4]{x^{3}}} \displaystyle \frac{\sqrt[4]{x}}{\sqrt[4]{x}}=\frac{\sqrt[4]{x}}{x}$
(c) $\displaystyle \frac{1}{\sqrt[3]{x^{4}}}=\frac{1}{\sqrt[3]{x^{3}x}}=\frac{1}{x\sqrt[3]{x}}=
\frac{1}{x\sqrt[3]{x}}\displaystyle \frac{\sqrt[3]{x^{2}}}{\sqrt[3]{x^{2}}} =\frac{\sqrt[3]{x^{2}}}{x\sqrt[3]{x^{3}}}=\frac{\sqrt[3]{x^{2}}}{x*x}=\frac{\sqrt[3]{x^{2}}}{x^{2}}$
