SOLUTION
We want write this as a rational exponent
[tex](\sqrt[5]{x^7})^3[/tex]
This simply means the 5th root of x to power 7 all raised to power 5.
First step is to write the root form to exponent form we have
[tex]\begin{gathered} \sqrt[5]{x^7}=(x^7)^{\frac{1}{5}^{}} \\ =(x^7)^{\times\frac{1}{5}^{}} \\ x^{\frac{7}{5}} \end{gathered}[/tex]
Next is the exponent 3, we have
[tex]\begin{gathered} (x^{\frac{7}{5}})^3 \\ (x^{\frac{7}{5}})^{\times3} \\ x^{\frac{21}{5}} \end{gathered}[/tex]
Hence the answer is
[tex]x^{\frac{21}{5}}[/tex]
