The expression that represents fifth root of x to the fourth power in exponential form is:
x to the four fifths power i.e. it is represented as: [tex]x^{\dfrac{4}{5}}[/tex]
We are asked to represent:
fifth root of x to the fourth power in exponential form
i.e. we have to represent : [tex]\sqrt[5]{x^4}[/tex] in exponential form.
We know that any expression of the form [tex]\sqrt[n]{x^m}[/tex] could also be represented as:
[tex]\sqrt[n]{x^m}=(x^m)^{\dfrac{1}{n}}=x^{\dfrac{m}{n}[/tex]
Here we have n=5 and m=4
Hence, the expression in exponential form is:
[tex]x^{\dfrac{4}{5}}[/tex]
