Given expression:
[tex]\sqrt[5]{(n+4)^{3}}[/tex]
To find:
The equivalent expression.
Solution:
[tex]\sqrt[5]{(n+4)^{3}}[/tex]
Apply radical rule:
[tex]$\sqrt[m]{a}=a^{\frac{1}{m}}[/tex]
Using this rule in the given expression:
[tex]\sqrt[5]{(n+4)^{3}}=\left((n+4)^{3}\right)^{\frac{1}{5}}[/tex]
Apply exponent rule:
[tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]
Using this rule:
[tex]\left((n+4)^{3}\right)^{\frac{1}{5}}=(n+4)^{3 \cdot \frac{1}{5}}[/tex]
On multiplying 3 and [tex]\frac{1}{5}[/tex], we get [tex]\frac{3}{5}[/tex].
[tex]=(n+4)^{\frac{3}{5}}[/tex]
The equivalent expression for the given expression is [tex](n+4)^{\frac{3}{5}}[/tex].
