how to prove the left side equation is equal to right side equation ?
[tex]cube root {8x^4}[\math]=[tex]2x^3sqrt{x}[\math]
why i can't form the equation correctly?
First of all, the LaTeX code you want is
\sqrt[3]{8x^4} = 2x^3\sqrt{x}
to get $\displaystyle \sqrt[3]{8x^4} = 2x^3\sqrt{x}$.
Now to answer your question... the left hand side does NOT equal the right hand side...
$\displaystyle \sqrt[3]{8x^4} = \sqrt[3]{8}\sqrt[3]{x^3}\sqrt[3]{x}$
$\displaystyle = 2x\sqrt[3]{x}$
$\displaystyle \neq 2x^3\sqrt{x}$.