Question

How to write radical form in rational form

Answer 1

The Rational form of
`\sqrt[4]{5^5}` is
`5^{(5)/(4)}`

Step-by-step explanation:

Given : Radical form as
`\sqrt[4]{5^5}`

We have to write the given radical form in rational form.

Consider the given radical form as
`\sqrt[4]{5^5}`

We know the rational form of a root form is
`\sqrt[n]{x} =x^{(1)/(n)}`

Thus, The given expression has n = 4 and x =
`5^5`

`\sqrt[4]{5^5}=(5^5)^{(1)/(4)}`

Also, Applying exponent rule, we have,

`(x^a)^b=x^ab`

Thus,
`5^{(5)/(4)}`

Thus, The Rational form of
`\sqrt[4]{5^5}` is
`5^{(5)/(4)}`

Answer 2

Answer:
5⁵/⁴

Step-by-step explanation:
Before we begin, remember the following:

`\sqrt[n]{x}` = x¹/ⁿ


`\sqrt[n]{x^a}` = xᵃ/ⁿ

The root form is known as the radical form while the power form is the rational form

Now, for the given:
We want to convert from the radical (root) form to the rational (power) form.
The given is:
4th root of 5⁵

Applying the above rules, we will find that the rational form is:
5⁵/⁴

Hope this helps :)