91影视

The given expressions are,

$$\begin{gathered} a)\frac{1}{\sqrt[3]{3}} \\ b)\sqrt[3]{\frac{5}{32}} \\ c)\frac{7}{\sqrt[3]{49b}} \end{gathered}$$

Now, to rationalize the expression first we will multiply the numerator and denominator by $\sqrt[3]{3^2}$.

$\frac{1}{\sqrt[3]{3}}=\frac{1脳\sqrt[3]{3^2}}{\sqrt[3]{3}脳\sqrt[3]{3^2}}$

On simplifying we get

$\frac{1脳\sqrt[3]{3^2}}{\sqrt[3]{3}脳\sqrt[3]{3^2}}=\frac{\sqrt[3]{9}}{3}$

Hence, the rationalization of the denominator is$\frac{\sqrt[3]{9}}{3}$.

Now, to rationalize the expression first we will rewrite the expression using quotient property and simplify.

$$\begin{gathered} \sqrt[3]{\frac{5}{32}}=\frac{\sqrt[3]{5}}{\sqrt[3]{32}} \\ =\frac{\sqrt[3]{5}}{2\sqrt[3]{4}} \end{gathered}$$

Multiplying the numerator and denominator by $\sqrt[3]{4^2}$.

$\frac{\sqrt[3]{5}}{2\sqrt[3]{4}}=\frac{\sqrt[3]{5}脳\sqrt[3]{4^2}}{2\sqrt[3]{4}脳\sqrt[3]{4^2}}$

Then on simplifying we get,

$\frac{\sqrt[3]{5}脳\sqrt[3]{4^2}}{2\sqrt[3]{4}脳\sqrt[3]{4^2}}=\frac{2\sqrt[3]{10}}{8}$

Finally removing the common factors.

$\frac{2\sqrt[3]{10}}{8}=\frac{\sqrt[3]{10}}{4}$

Hence, the rationalization of the denominator is$\frac{\sqrt[3]{10}}{4}$.

Now, to rationalize the expression first we will multiply the numerator and denominator by $\sqrt[3]{{\left(49\right)}^2{b}^2}$.

$\frac{7}{\sqrt[3]{49b}}=\frac{7脳\sqrt[3]{{\left(49\right)}^2{b}^2}}{\sqrt[3]{49b}脳\sqrt[3]{{\left(49\right)}^2{b}^2}}$

On simplifying we get,

$\frac{7脳\sqrt[3]{{\left(49\right)}^2{b}^2}}{\sqrt[3]{49b}脳\sqrt[3]{{\left(49\right)}^2{b}^2}}=\frac{49\sqrt[3]{7b^2}}{49b}$

Then removing the common factors.

$\frac{49\sqrt[3]{7b^2}}{49b}=\frac{\sqrt[3]{7b^2}}{b}$

Hence, the rationalization of the denominator is$\frac{\sqrt[3]{7b^2}}{b}$.