Given:

Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
![A^{(x)/(y)}=\sqrt[y]{A^x}](https://img.qammunity.org/2023/formulas/mathematics/college/mkl1ia0dagfc4stg967nsiu45vadufxgx4.png)
I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
![\begin{gathered} 7^{(3)/(4)}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{(1)/(4)}=343^{((1)/(2)*(1)/(2))} \\ =343^{((1)/(2)*(1)/(2))}=\sqrt[]{343^{(1)/(2)}} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/8gwlr8zy2wbmbaxs5tbvskcw0trzftf59f.png)
Now, we have our value in the square root form as:
![\sqrt[]{343^{(1)/(2)}}=\sqrt[]{7^{(3)/(2)}}](https://img.qammunity.org/2023/formulas/mathematics/college/v82lalcit2gb3kpovso3ydc7o7yzx65588.png)