Given:
[tex]x^{\frac{7}{3}}[/tex]To get the equivalent using the law of indices that state that
[tex]a^{\frac{m}{n}}=(\sqrt[n]{a})^m[/tex]Then, it follows that
[tex]x^{\frac{7}{3}}=\text{ (}\sqrt[3]{x})^7[/tex]From the option provided
[tex]\begin{gathered} x\text{.}\sqrt[3]{x^2}=xx^{\frac{2}{3}} \\ =x^{(1+\frac{2}{3})}=x^{(\frac{3}{3}+\frac{2}{3})}=x^{\frac{5}{3}} \\ \text{since x}^{\frac{5}{3}}\ne x^{\frac{7}{3}} \end{gathered}[/tex]Option A is wrong
Let us try option B
[tex]\begin{gathered} x^2\text{.(}\sqrt[3]{x})=x^2\times x^{\frac{1}{3}}=x^{(2+\frac{1}{3})} \\ =x^{(\frac{6}{3}+\frac{1}{3})}=x^{(\frac{6+1}{3})^{}} \\ =x^{\frac{7}{3}} \\ \end{gathered}[/tex][tex]undefined[/tex]Option B is the correct answer
