Given expression:
![\sqrt[5]{(n+4)^(3)}](https://img.qammunity.org/2021/formulas/mathematics/high-school/2a5urdvu47e6s67mxq5r8aot1aypkwb8tj.png)
To find:
The equivalent expression.
Solution:
![\sqrt[5]{(n+4)^(3)}](https://img.qammunity.org/2021/formulas/mathematics/high-school/2a5urdvu47e6s67mxq5r8aot1aypkwb8tj.png)
Apply radical rule:
![$\sqrt[m]{a}=a^{(1)/(m)}](https://img.qammunity.org/2021/formulas/mathematics/high-school/zkrkusgt37e1po6dl6hof53de4vjz0qivw.png)
Using this rule in the given expression:
![\sqrt[5]{(n+4)^(3)}=\left((n+4)^(3)\right)^{(1)/(5)}](https://img.qammunity.org/2021/formulas/mathematics/high-school/csiz0lute6i84jnbvz9j3erbjwupunc2b2.png)
Apply exponent rule:

Using this rule:

On multiplying 3 and
, we get
.

The equivalent expression for the given expression is
.