Step 1

Given: \(\sqrt[3]{x}=2\sqrt[4]{x}\)

For finding solution of given equation, we take power 12 both side and simplify it

Step 2

So,

\({\sqrt[3]{x}}^{12}=2\sqrt[4]{x}^{12}\)

\(\displaystyle{x}^{{{4}}}={2}^{{{12}}}{x}^{{{3}}}\)

\(\displaystyle{x}^{{{4}}}-{2}^{{{12}}}{x}^{{{3}}}={0}\)

\(\displaystyle{x}^{{{3}}}{\left({x}-{2}^{{{12}}}\right)}={0}\)

\(\displaystyle{x}={0},{2}^{{{12}}}\)

Hence, solution of given equation is \(\displaystyle{x}={0},{2}^{{{12}}}\).