To rationalize: Each numerator. Assume that variables represent positive real numbers. Given: An expression :...

Concept used:
In order to rationalize the numerator of an expression, we multiply in the numerator and denominator with such a term/expression such that we don't have any radicals left in the numerator upon simplifying.
Calcucation:
Let us rationalize the numerator as shown below:
${\displaystyle \frac{\sqrt[3]{9}}{7}}$ (Given expression)
${\displaystyle \Rightarrow \frac{\sqrt[3]{9}}{7}\cdot \frac{\sqrt[3]{3}}{\sqrt[3]{3}}\text{(multiplying fraction by}{\displaystyle \sqrt[3]{3})}}$
${\displaystyle \Rightarrow \frac{\sqrt[3]{9}\cdot \sqrt[3]{3}}{7\cdot \sqrt[3]{3}}}$
${\displaystyle \Rightarrow \frac{\sqrt[3]{9\cdot 3}}{7\sqrt[3]{3}}(Applyinteger\sqrt[n]{a}\cdot \sqrt[n]{b}=\sqrt[n]{ab})}$
${\displaystyle \Rightarrow \frac{\sqrt[3]{27}}{7\sqrt[3]{3}}}$
${\displaystyle \Rightarrow \frac{\sqrt[3]{3^3}}{7\sqrt[3]{3}}}$
${\displaystyle \Rightarrow \frac{3}{7\sqrt[3]{3}}(Applyinteger\sqrt[n]{a^n}=a)}$
Therefore, the rationalized form of the given expression would be ${\displaystyle \frac{3}{7\sqrt[3]{3}}.}$