Question

How to put 7^3/4 in radical form

Answer 1

Given:

`7^{(3)/(4)}`

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}`

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}`

Now, we have our value in the square root form as:

`\sqrt[]{343^{(1)/(2)}}=\sqrt[]{7^{(3)/(2)}}`