Question

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

Answer 1

Option C, D, E are the correct options.

Explanation:

The given expression is
`x^{(8)/(5)}`

Now we will check for each option given

A.
`(x^(5))^{(1)/(8)}=x^{(5)/(8)}`

Wrong option.

B.
`\sqrt[8]{x^(5)}=x^{(5)/(8)}`

Wrong option

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

Correct option

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

Correct option

E.
`(x^(8))^{(1)/(5)}=x^{(8)/(5)}`

Correct option

F.
`(\sqrt[8]{x})^(5)=x^{(5)/(8)}`

Wrong option

Answer 2

Answer :

C , D, E are equivalent to
`x^{(8)/(5) }`.

Step by step explanation :

Given:
`x^{(8)/(5) }`.

To find : Which of the following choices are equivalent to the expression below .

Solution : We have given that
`x^{(5)/(8) }`.

Now , we will check all option .

By exponent rule :
`(a^(b) )^c= a^(bc)`

A .
`(x^(5) )^(1)/(8)` =
`x^{(5)/(8) }`.

Wrong

B .
`\sqrt[8]{x^(5) }` =
`x^{(5)/(8) }`.

Wrong

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

Correct

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

Correct

E.
`(x^(8) )^(1)/(5)` =
`x^{(8)/(5) }`.

Correct

F.
`(\sqrt[8]{x} )^5` =
`x^{(5)/(8) }`.

Wrong .

Therefore, C , D, E are equivalent to
`x^{(8)/(5) }`.