Answer:
The choices which are equivalent to the given expression is:
[tex]C.\ \ (\sqrt[5]{x})^8\\ \\D.\ \ \sqrt[5]{x^8}\\\\E.\ \ (x^8)^{\frac{1}{5}}[/tex]
Step-by-step explanation:
We are given a expression in terms of variable x as:
[tex]x^{\frac{8}{5}}[/tex]
We know that any expression of the form: [tex]x^{\frac{m}{n}}[/tex] could also be represented by:
[tex]x^{\frac{m}{n}=(x^m)^{\frac{1}{n}}=\sqrt[n]{x^m}[/tex]
which is nothing but equivalent to:
[tex]x^{\frac{m}{n}}=(x^{\frac{1}{n}})^m=(\sqrt[n]{x})^m[/tex]
Here we have: n=5 and m=8
Hence, the equivalent expressions are:
Options: C,D and E.
