Answer
$\frac{\sqrt[4]{189x^3 }}{3x}$.
Work Step by Step
The given expression is
$=\sqrt[4]{\frac{7}{3x}}$
Use quotient rule.
$=\frac{\sqrt[4]{7}}{\sqrt[4]{3x}}$
Multiply the numerator and the denominator by $\sqrt[4]{(3x)^3}$
$=\frac{\sqrt[4]{7}}{\sqrt[4]{3x}}\cdot \frac{\sqrt[4]{(3x)^3}}{\sqrt[4]{(3x)^3}}$
Use product rule.
$=\frac{\sqrt[4]{7\cdot(3x)^3 }}{\sqrt[4]{(3x)\cdot (3x)^3}}$
Simplify.
$=\frac{\sqrt[4]{7\cdot27x^3 }}{\sqrt[4]{(3x)^4}}$
$=\frac{\sqrt[4]{189x^3 }}{3x}$.
