Question

Which of the following choices are equivalent to the expression below ?

Answer 1

I know so for sure its D and F cuz its being divided by 5 and still holds x with 8 as a if it were 8x, im not sure if another one is there but i know those two work.

Answer 2

The choices which are equivalent to the given expression is:

`C.\ \ (\sqrt[5]{x})^8\\ \\D.\ \ \sqrt[5]{x^8}\\\\E.\ \ (x^8)^{(1)/(5)}`

Explanation:

We are given a expression in terms of variable x as:

`x^{(8)/(5)}`

We know that any expression of the form:
`x^{(m)/(n)}` could also be represented by:

`x^{(m)/(n)=(x^m)^{(1)/(n)}=\sqrt[n]{x^m}`

which is nothing but equivalent to:

`x^{(m)/(n)}=(x^{(1)/(n)})^m=(\sqrt[n]{x})^m`

Here we have: n=5 and m=8

Hence, the equivalent expressions are:

Options: C,D and E.