Question

Which of the following represents fifth root of x to the fourth power in exponential form?

Answer 1

Question says that which of the following represents fifth root of x to the fourth power in exponential form?

Given choices are missing but still we can do this problem.

fifth root means index of the root is 5.

"to the fourth power" means overall exponent is 4.

So the given problem can be written as:

$\sqrt[5]{x^4}$

We know that nth root means exponent 1/n

so 5th root means exponent 1/5

Now the given problem can be written as:

$\left(x^4\right)^{\left(\frac{1}{5}\right)}$

$x^{\left(4\cdot\frac{1}{5}\right)}$

$x^{\frac{4}{5}}$

Hence final answer is $x^{\frac{4}{5}}$.