Answer and explanation
We have given equation
![\frac{6x^3}{\sqrt[3]{27x^6}}](https://img.qammunity.org/2020/formulas/mathematics/high-school/r3y8yceqo2b78ccl4z6vb15d1o7ru0xemg.png)
We have to prove that after operation it will be equal to 2x
We know that cube root of 27 is 3
And cube root of
is

So we can write the expression
![\frac{6x^3}{\sqrt[3]{27x^6}}=(6x^3)/(3x^2)=2x](https://img.qammunity.org/2020/formulas/mathematics/high-school/vxox0k8zppglyjypxu9pbcj73cbigowaao.png)
So after doing operation on the given expression the result will be 2x
Hence proved