Question

Rewrite the radical expression as an expression with rational exponents. fourth root of x to the power of 5

A.4X^5
B.5X^4
C.X^5/4
D.X^4/5

Answer 1

The correct option is C) X^(5/4).

Explanation:

Consider the provided radical expression.

`\sqrt[4]{x^5}`

Now we need to convert the radical expression into rational expression.

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

By using the above formula we can rewrite the expression as shown:

`\sqrt[4]{x^5}`

`(\sqrt[4]{x})^5`

`(x)^{(5)/(4)}`

Hence, the required rational exponent is
`(x)^{(5)/(4)}`

Thus, the correct option is C) X^(5/4).

Answer 2

C

Explanation:

We simply need to remember this rule shown below:

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

So expression to change is
`\sqrt[4]{x^5}`

By using the law, we can rewrite this as:

`\sqrt[4]{x^5} =x^{(5)/(4)}`

Correct choice is C