Rationalize the denominator: 1/cube root(a)

$$\\\dfrac{1}{\sqrt[3]{a}}\\\\\\ =\dfrac{1}{a^{1/3}}\\\\\\ =\dfrac{1}{a^{1/3}}\times \dfrac{a^{2/3}}{a^{2/3}}\\\\\\ =\dfrac{a^{2/3}}{a^{1/3+2/3}}\\\\\\ =\dfrac{a^{2/3}}{a^{1}}\\\\\\ =\dfrac{\sqrt[3]{a^2}}{a}\\\\\\ $Which is exactly what geno said in the first place!$$ $

To remove the radical from the denominator, multiply both the numerator and the denominator by a value that makes the denominator whole.

If the denominator is cube root(a) multiply the numerator and denominator by cube root(a²).

The numerator becomes the cube root(a²) while the denominator becomes the cube root(a³), which is just a.

So the answer is: cube root(a²) / a.