Option C:
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Solution:
Given expression is [tex]\sqrt[5]{34}[/tex].
To write the given expression in rational exponent form.
Using rational exponent rule:
[tex]$\sqrt[n]{a^m} =a^{\frac{m}{n} }[/tex]
i. e. [tex]$\sqrt[\text{root}]{a^\text{power}} =a^{\frac{\text{power}}{\text{root}} }[/tex]
Given [tex]\sqrt[5]{34}[/tex]
Here, root is 5 and power is 1.
Write it using the rational exponent rule,
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Therefore option C is the correct answer.
Hence [tex]$\sqrt[5]{34} =34^{\frac{1}{5} }.[/tex]
