Question

Rewrite the expression with a rational exponent as a radical expression.

(4^2/5)^1/4


a.)^10sqrt4
b.)^4sqrt4
c.)^5sqrt4^2
d.)sqrt4^10


sqrt=square root

Answer 1

First option is correct.

`\sqrt[10]{4}`

Explanation:

Given:

The given expression is
`(4^{(2)/(5)})^{(1)/(4)}`

We write the given expression with a rational exponent as a radical expression such as.

`=(4^{(2)/(5)})^{(1)/(4)}`

Simplify the above equation by multiplication of powers.

`=(4^{(2)/(5)* (1)/(4)})`

`=(4^{(1)/(5)* (1)/(2)})`

`=(4^{(1)/(5* 2)})`

`=(4^{(1)/(10)})`

`=\sqrt[10]{4}`

Therefore, The answer is
`=\sqrt[10]{4}`.