Answer:
Given the expression: [tex](27)^{\frac{1}{5}}[/tex]
Using the rule of radical and exponent power:
[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]
We can write 27 as:
[tex]27 = 3 \cdot 3 \cdot 3 = 3^3[/tex]
Then;
[tex](27)^{\frac{1}{5}}[/tex]
⇒[tex](3^3)^{\frac{1}{5}}[/tex]
⇒[tex](3)^{\frac{3}{5}}[/tex]
Apply the rule:
[tex]\sqrt[5]{3^3}[/tex]
Therefore, the radical expression that is equivalent to the expression [tex](27)^{\frac{1}{5}}[/tex] is [tex]\sqrt[5]{3^3}[/tex]
