Question

Rewrite the following radical expression in rational exponent form. (√x)5

Answer 1

If you meant:

`( √(x))^5`

Then, let's change the square to read:

`(x^ (1)/(2))^5`

Now, we can just multiply the two powers, and your answer is:

`x^ (5)/(2)`

Hope I helped.

Answer 2

The rational exponent form of given expression is
`x^{(5)/(2)}`.

Explanation:

A number is called a rational number if it can be defined as p/q, where p and q are real numbers and q≠0.

The given expression is

`(√(x))^5`

It can be written as

`(√(x))^5=(x^{(1)/(2)})^5`
`[\because √(x)=(x)^{(1)/(2)}]`

Using the power property of exponent we get

`(√(x))^5=x^{(5)/(2)}`
`[\because (x^m)^n=x^(mn)]`

Here
`(5)/(2)` is a rational number.

Therefore the rational exponent form of given expression is
`x^{(5)/(2)}`.