Question

Wich expression represents 5/34 in rational exponent form

Answer 1

Option C:

$\sqrt[5]{34} =34^{\frac{1}{5} }$

Solution:

Given expression is $\sqrt[5]{34}$.

To write the given expression in rational exponent form.

Using rational exponent rule:

$\sqrt[n]{a^m} =a^{\frac{m}{n} }$

i. e. $\sqrt[\text{root}]{a^\text{power}} =a^{\frac{\text{power}}{\text{root}} }$

Given  $\sqrt[5]{34}$

Here, root is 5 and power is 1.

Write it using the rational exponent rule,

$\sqrt[5]{34} =34^{\frac{1}{5} }$

Therefore option C is the correct answer.

Hence $\sqrt[5]{34} =34^{\frac{1}{5} }.$