Respuesta :

Louli
Answer:
5⁵/⁴

Explanation:
Before we begin, remember the following:
[tex] \sqrt[n]{x} [/tex] = x¹/ⁿ

[tex] \sqrt[n]{x^a} [/tex] = 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 :)

Answer:

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

Step-by-step explanation:

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

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

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

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

Thus, The given expression has n = 4 and x = [tex]5^5[/tex]

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

Also, Applying exponent rule, we have,

[tex](x^a)^b=x^ab[/tex]

Thus, [tex]5^{\frac{5}{4}}[/tex]

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

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