Question

How to write radical form in rational form

Answer 1

Answer:

The Rational form of $\sqrt[4]{5^5}$ is  $5^{\frac{5}{4}}$

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 $\sqrt[n]{x} =x^{\frac{1}{n}}$

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

$\sqrt[4]{5^5}=(5^5)^{\frac{1}{4}}$

Also, Applying exponent rule, we have,

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

Thus, $5^{\frac{5}{4}}$

Thus, The Rational form of $\sqrt[4]{5^5}$ is  $5^{\frac{5}{4}}$

Answer 2

Answer:
5⁵/⁴

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 :)