Answer:[tex]\frac{\sqrt[3]{100x}}{5}[/tex]
Step-by-step explanation:
Given expression : cube root of [tex]\frac{4x}{5}[/tex]
which is equivalent to [tex]\sqrt[3]{\frac{4x}{5}}[/tex]
To simplify this we need to make denominator a perfect cube.
So multiply and divide 25 inside the cube root, so that the denominator will become a perfect cube of 5.
[tex]\sqrt[3]{\frac{4x}{5}}=\sqrt[3]{\frac{4x}{5}\times\frac{25}{25}}\\=\sqrt[3]{\frac{100x}{125}}\\=\sqrt[3]{\frac{100x}{5^3}}\\=\frac{\sqrt[3]{100x}}{5}[/tex]