We conclude that:
   Â
Hence, option A i.e.
 is true.  Â
Step-by-step explanation:
Given the expression
![\left(\:\:\frac{x^4}{\frac{3x^2}{3}}\right)^{\frac{1}{3}}](/tpl/images/1057/2724/30eb5.png)
Apply exponent rule: Â ![\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}](/tpl/images/1057/2724/2ae26.png)
![\left(\frac{x^4}{\frac{3x^2}{3}}\right)^{\frac{1}{3}}=\frac{\left(x^4\right)^{\frac{1}{3}}}{\left(\frac{3x^2}{3}\right)^{\frac{1}{3}}}](/tpl/images/1057/2724/8709d.png)
      Â
    ∵ ![\:\:\:\left(x^4\right)^{\frac{1}{3}}=x^{\frac{4}{3}}](/tpl/images/1057/2724/80dbc.png)
       ![=\frac{x^{\frac{4}{3}}}{\frac{\left(3x^2\right)^{\frac{1}{3}}}{3^{\frac{1}{3}}}}](/tpl/images/1057/2724/30d7f.png)
       ![=\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}](/tpl/images/1057/2724/42b5e.png)
Apply exponent rule: Â Â ![\frac{x^a}{x^b}=x^{a-b}](/tpl/images/1057/2724/78c7e.png)
      Â
    Â
       ![=x^{\frac{2}{3}}\\](/tpl/images/1057/2724/abbc1.png)
Therefore, we conclude that:
   Â
Hence, option A i.e.
 is true.                    Â