#### Answer

$\dfrac{\sqrt[3]{100}}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt[3]{\dfrac{4}{5}}
,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{4}{5}\cdot\dfrac{5^2}{5^2}}
\\\\=
\sqrt[3]{\dfrac{4(5^2)}{5^3}}
\\\\=
\sqrt[3]{\dfrac{4(25)}{5^3}}
\\\\=
\sqrt[3]{\dfrac{100}{5^3}}
.\end{array}
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{100}}{\sqrt[3]{5^3}}
\\\\=
\dfrac{\sqrt[3]{100}}{5}
.\end{array}