How do you simplify root3(54x)-root3(2x^4)?

Sep 1, 2016

$\left(3 - x\right) \sqrt[3]{2 x}$

Explanation:

you can substitute 54 by the product of its factors $2 \cdot {3}^{3}$ and have the equivalent expression:

$\sqrt[3]{2 \cdot {3}^{3} x} - \sqrt[3]{2 {x}^{3} \cdot x}$

you can partially simplify:

$\sqrt[3]{2 x} \cdot \left(\sqrt[3]{{3}^{3}}\right) - \sqrt[3]{2 x} \cdot \sqrt[3]{{x}^{3}}$

$3 \sqrt[3]{2 x} - x \sqrt[3]{2 x}$

$\left(3 - x\right) \sqrt[3]{2 x}$