Answer
$\sqrt[4]{\dfrac{16}{9x^{7}}}=\dfrac{2\sqrt[4]{9x}}{3x^{2}}$
Work Step by Step
$\sqrt[4]{\dfrac{16}{9x^{7}}}$
Rewrite this expression as $\dfrac{\sqrt[4]{16}}{\sqrt[4]{9x^{7}}}$ and simplify it:
$\sqrt[4]{\dfrac{16}{9x^{7}}}=\dfrac{\sqrt[4]{16}}{\sqrt[4]{9x^{7}}}=\dfrac{2}{x\sqrt[4]{9x^{3}}}=...$
Multiply the fraction by $\dfrac{\sqrt[4]{9x}}{\sqrt[4]{9x}}$ and simplify:
$...=\dfrac{2}{x\sqrt[4]{9x^{3}}}\cdot\dfrac{\sqrt[4]{9x}}{\sqrt[4]{9x}}=\dfrac{2\sqrt[4]{9x}}{x\sqrt[4]{81x^{4}}}=\dfrac{2\sqrt[4]{9x}}{x(3x)}=\dfrac{2\sqrt[4]{9x}}{3x^{2}}$
