Question

Rewrite the radical expression as an expression with rational exponents four square root X to the fifth

Answer 1

For this case we must write algebraically the following expression:

"four square root x to the fifth"

We have to:

square root x is represented as:
`\sqrt {x}`

Then, the expression will be:

`4 \sqrt {x ^ 5}`

Equivalently, according to the property of powers and roots:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

We have:

`4x ^ {\frac {5} {2}}`

ANswer:

`4 \sqrt {x ^ 5}\\4x ^ {\frac {5} {2}}`

Answer 2

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

Explanation:

We are asked to rewrite the radical expression as an expression with rational exponents.

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

Using exponent property
`\sqrt[n]{a^m}=a^{(m)/(n)}`, we can rewrite our given expression as:

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

Therefore, our required expression would be
`x^{(5)/(4)}`.